User:Tomruen/Convex uniform tetracomb

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Regular and uniform honeycombs[edit]

There are five fundamental affine Coxeter groups that generate regular and uniform tessellations in 4-space.[1]

# Coxeter group Coxeter-Dynkin diagram
1 A~4 [(3,3,3,3,3)] [3[5]] CD downbranch-00.pngCD downbranch-33.pngCD righttriangleopen 000.png
2 B~4 [4,3,3,4] CDW dot.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 4.pngCDW dot.png
3 C~4 [4,3,31,1] h[4,3,3,4] CD dot.pngCD 4.pngCD dot.pngCD 3b.pngCD downbranch-00.pngCD 3b.pngCD dot.png
4 D~4 [31,1,1,1] q[4,3,3,4] CDT dot.pngCDT 3a.pngCDT branch000.pngCDT 3a.pngCDT dot.png
5 F~4 [3,4,3,3] h[4,3,3,4] CDW dot.pngCDW 3b.pngCDW dot.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.png

There are three regular honeycomb of Euclidean 4-space:

  1. tesseractic honeycomb, with symbols {4,3,3,4}, CDW ring.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 4.pngCDW dot.png = CD ring.pngCD 4.pngCD dot.pngCD 3b.pngCD downbranch-00.pngCD 3b.pngCD dot.png. There are 19 uniform honeycombs in this family.
  2. 24-cell honeycomb, with symbols {3,4,3,3}, CDW ring.pngCDW 3b.pngCDW dot.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.png. There are 31 uniform honeycombs in this family.
  3. 16-cell honeycomb, with symbols {3,3,4,3}, CDW ring.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.png

Other families that generate uniform honeycombs:

  • There are 23 uniform honeycombs, 4 unique in the 16-cell honeycomb family. With symbols h{4,32,4} it is geometrically identical to the 16-cell honeycomb, CDW hole.pngCDW 4.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 3b.pngCDW dot.pngCDW 4.pngCDW dot.png = CD dot.pngCD 4.pngCD dot.pngCD 3b.pngCD downbranch-00.pngCD 3b.pngCD ring.png
  • There are 7 uniform honeycombs from the A~4, CD downbranch-00.pngCD downbranch-33.pngCD righttriangleopen 000.png family, all unique.
  • There are 9 uniform honeycombs in the D~4: [31,1,1,1] CDT dot.pngCDT 3a.pngCDT branch000.pngCDT 3a.pngCDT dot.png family, all repeated in other families, including the 16-cell honeycomb.

Non-Wythoffian uniform tessellations in 4-space also exist by elongation (inserting layers), and gyration (rotating layers) from these reflective forms.

The single-ringed tessellations are given below, indexed by Olshevsky's listing.

Duoprismatic forms

  • B~2xB~2: [4,4]x[4,4] = [4,3,3,4] CDW dot.pngCDW 4.pngCDW dot.pngCDW 4.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW 4.pngCDW dot.pngCDW 4.pngCDW dot.png = CDW dot.pngCDW 4.pngCDW dot.pngCDW 3.pngCDW dot.pngCDW 3.pngCDW dot.pngCDW 4.pngCDW dot.png (Same as tesseractic honeycomb family)
  • B~2xH~2: [4,4]x[6,3] CDW dot.pngCDW 4.pngCDW dot.pngCDW 4.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW 6.pngCDW dot.pngCDW 3.pngCDW dot.png
  • H~2xH~2: [6,3]x[6,3] CDW dot.pngCDW 6.pngCDW dot.pngCDW 3.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW 6.pngCDW dot.pngCDW 3.pngCDW dot.png
  • A~2xB~2: [Δ]x[4,4] CD righttriangle-000.pngCDW 2.pngCDW dot.pngCDW 4.pngCDW dot.pngCDW 4.pngCDW dot.png (Same forms as [6,3]x[4,4])
  • A~2xH~2: [Δ]x[6,3] CD righttriangle-000.pngCDW 2.pngCDW dot.pngCDW 6.pngCDW dot.pngCDW 3.pngCDW dot.png (Same forms as [6,3]x[6,3])
  • A~2xA~2: [Δ]x[Δ] CD righttriangle-000.pngCDW 2.pngCD righttriangle-000.png (Same forms as [6,3]x[6,3])

Prismatic forms

  • B~3xI~1: [4,3,4]x[∞] CDW dot.pngCDW 4.pngCDW dot.pngCDW 3.pngCDW dot.pngCDW 4.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW infin.pngCDW dot.png
  • D~3xI~1: [4,31,1]x[∞] CD dot.pngCD 3.pngCD downbranch-00.pngCD 4.pngCD dot.pngCD 2.pngCD dot.pngCD infin.pngCD dot.png
  • A~3xI~1: CD downbranch-00.pngCD downbranch-33.pngCD downbranch-00.pngCD 2.pngCD dot.pngCD infin.pngCD dot.png

Noncompact prismatic forms

  • A3xI~1: [3,3]x[∞] - CDW dot.pngCDW 3.pngCDW dot.pngCDW 3.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW infin.pngCDW dot.png
  • B3xI~1: [4,3]x[∞] - CDW dot.pngCDW 4.pngCDW dot.pngCDW 3.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW infin.pngCDW dot.png
  • H3xI~1: [5,3]x[∞] - CDW dot.pngCDW 5.pngCDW dot.pngCDW 3.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW infin.pngCDW dot.png
  • I~1xI~1xI2r: [∞] x [∞] x [r] = [4,4]x[r] - CDW dot.pngCDW infin.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW infin.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW r.pngCDW dot.png = CDW dot.pngCDW 4.pngCDW dot.pngCDW 4.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW r.pngCDW dot.png

Non-Wythoffian forms[edit]

The non-Wythoffian forms are built as stacked composites of these prismatic noncompact groups:

  • I2pxI~1xA1: [p]x[∞]x[ ] - CDW dot.pngCDW p.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW infin.pngCDW dot.pngCDW 2.pngCDW dot.png (Prism column)
  • D~3xA1: [4,31,1]x[ ] CD dot.pngCD 3.pngCD downbranch-00.pngCD 4.pngCD dot.pngCD 2.pngCD dot.png (Prism slab)
  • A~3xA1: CD downbranch-00.pngCD downbranch-33.pngCD downbranch-00.pngCD 2.pngCD dot.png (Prism slab)
  • A~2xI2p: [Δ]x[p] CD righttriangle-000.pngCD 2.pngCD dot.pngCD p.pngCD dot.png (Prism slab)
  • B~2xI2p: [4,4]x[p] CDW dot.pngCDW 4.pngCDW dot.pngCDW 4.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW p.pngCDW dot.png (Prism slab)
  • H~2xI2p: [6,3]x[p] CDW dot.pngCDW 6.pngCDW dot.pngCDW 3.pngCDW dot.pngCDW 2.pngCDW dot.pngCDW p.pngCDW dot.png (Prism slab)


B~4 [4,3,3,4] family[edit]

# Coxeter-Dynkin
andSchläfli
symbols
Name Facets by location: [4,3,3,4]
4 3 2 1 0
CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.png
[4,3,3]
CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel 2.pngCDel node.png
[4,3]×[ ]
CDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.png
[4]×[4]
CDel node.pngCDel 2.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
[ ]×[3,4]
CDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
[3,3,4]
1 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0{4,3,3,4}
Tesseractic honeycomb {4,3,3}
Schlegel wireframe 8-cell.png
- - - -
87 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t1{4,3,3,4}
Rectified tesseractic honeycomb t1{4,3,3}
Schlegel half-solid rectified 8-cell.png
- - - {3,3,4}
Schlegel wireframe 16-cell.png
88 CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t2{4,3,3,4}
Birectified tesseractic honeycomb
(Same as 24-cell honeycomb {3,4,3,3})
t1{3,3,4}
Schlegel wireframe 24-cell.png
- - - t1{3,3,4}
Schlegel wireframe 24-cell.png
89 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,1{4,3,3,4}
Truncated tesseractic honeycomb t0,1{4,3,3} - - - {3,3,4}
90 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,2{4,3,3,4}
Cantellated tesseractic honeycomb
(Small prismatotesseractic honeycomb)
t0,2{4,3,3} - - {}x{3,4} t1{3,3,4}
91 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
t0,3{4,3,3,4}
Runcinated tesseractic honeycomb
(Small diprismatotesseractic honeycomb)
92 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t1,2{4,3,3,4}
Bitruncated tesseractic honeycomb
93 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
t1,3{4,3,3,4}
Bicantellated tesseractic honeycomb
(Same as Rectified 24-cell honeycomb t1{3,4,3,3})
[1] CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png
t0,4{4,3,3,4}
Stericated tesseractic honeycomb
(same as tesseractic honeycomb)
94 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,1,2{4,3,3,4}
Cantitruncated tesseractic honeycomb
(Great prismatotesseractic honeycomb)
95 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
t0,1,3{4,3,3,4}
Runcitruncated tesseractic honeycomb
(Small tomocubic-diprismatotesseractic honeycomb)
96 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png
t0,1,4{4,3,3,4}
Steritruncated tesseractic honeycomb
(Tomotesseractic-diprismatotesseractic honeycomb)
97 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
t0,2,3{4,3,3,4}
Runcicantellated tesseractic honeycomb
(Rhombitesseractic-diprismatotesseractic honeycomb)
98 CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png
t0,2,4{4,3,3,4}
Stericantellated tesseractic honeycomb
(Small rhombitesseractic-prismatotesseractic honeycomb)
99 CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
t1,2,3{4,3,3,4}
Bicantitruncated tesseractic honeycomb
(Same as Truncated 24-cell honeycomb, t0,1{3,4,3,3} )
100 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
t0,1,2,3{4,3,3,4}
Runcicantitruncated tesseractic honeycomb
(Great diprismatotesseractic honeycomb)
101 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.png
t0,1,2,4{4,3,3,4}
Stericantitruncated tesseractic honeycomb
(Great rhombitesseractic-prismatotesseractic honeycomb)
102 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.png
t0,1,3,4{4,3,3,4}
Steriruncitruncated tesseractic honeycomb
(Great tomocubic-diprismatotesseractic honeycomb)
103 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.png
t0,1,2,3,4{4,3,3,4}
Omnitruncated tesseractic honeycomb

C~4 [31,1,3,4] family[edit]

There are 23 honeycombs in this family,[2] all listed below.

# Coxeter-Dynkin
andSchläfli
symbols
File:CDel B5 nodes.png
Name Facets by location: [31,1,3,4]
4 3 2 1 0
CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
[3,3,4]
CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.png
[31,1,1]
CDel nodes.pngCDel split2.pngCDel node.pngCDel 2.pngCDel node.png
[3,3]×[ ]
CDel node.pngCDel 2.pngCDel node.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.png
[ ]×[3]×[ ]
CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
[3,3,4]
104 CDel nodes 10.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
{31,1,3,4}
16-cell honeycomb {3,3,4}
Schlegel wireframe 16-cell.png
{31,1,1}
Schlegel wireframe 16-cell.png
- - -
105 CDel nodes.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,1{31,1,3,4}
Truncated 16-cell honeycomb
(Same as truncated 16-cell honeycomb, t0,1{3,3,4,3})
106 CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,2{31,1,3,4}
Cantellated 16-cell honeycomb
(Same as birectified 16-cell honeycomb)
107 CDel nodes.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,1,2{31,1,3,4}
Cantitruncated 16-cell honeycomb
(Same as bitruncated 16-cell honeycomb)
108 CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,3{31,1,3,4}
Runcinated 16-cell honeycomb
(Small diprismatodemitesseractive honeycomb)
109 CDel nodes.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,1,3{31,1,3,4}
Runcitruncated 16-cell honeycomb
(Small prismato16-cell honeycomb)
110 CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,2,3{31,1,3,4}
Runcicantellated 16-cell honeycomb
(Great prismato16-cell honeycomb)
111 CDel nodes.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,1,2,3{31,1,3,4}
Runcicantitruncated 16-cell honeycomb
(Great diprismato16-cell honeycomb)
[88] CDel nodes.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t1{31,1,3,4}
Rectified 16-cell honeycomb
(Same as 24-cell honeycomb, {3,4,3,3})
(Also birectified tesseractic honeycomb)
t1{3,3,4}
Schlegel wireframe 24-cell.png
t1{31,1,1}

Schlegel wireframe 24-cell.png

- - t1{3,3,4}
Schlegel wireframe 24-cell.png
[87] CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t2{31,1,3,4}
Same as rectified tesseractic honeycomb t1{4,3,3}
Schlegel half-solid rectified 8-cell.png
{31,1,1}
Schlegel wireframe 16-cell.png
- - t1{4,3,3}
Schlegel half-solid rectified 8-cell.png
[1] CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t3{31,1,3,4}
Same as tesseractic honeycomb {4,3,3}
Schlegel wireframe 8-cell.png
- - - {4,3,3}
Schlegel wireframe 8-cell.png
[87] CDel nodes 01.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,4{31,1,3,4}
(Same as Rectified tesseractive honeycomb)
[92] CDel nodes.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t1,2{31,1,3,4}
(Same as bitruncated tesseractic honeycomb)
[90] CDel nodes.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t1,3{31,1,3,4}
(Same as cantellated tesseractic honeycomb)
[89] CDel nodes.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t2,3{31,1,3,4}
(Same as truncated tesseractic honeycomb)
[92] CDel nodes 01.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,1,4{31,1,3,4}
(Same as bitruncated tesseractic honeycomb)
[93] CDel nodes 01.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,2,4{31,1,3,4}
(Same as rectified 24-cell honeycomb)
(Also bicantellated tesseractic honeycomb)
[91] CDel nodes 01.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,3,4{31,1,3,4}
(Same as runcinated tesseractic honeycomb)
[94] CDel nodes.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t1,2,3{31,1,3,4}
(Same as cantitruncated tesseractic honeycomb)
[99] CDel nodes 01.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,1,2,4{31,1,3,4}
(Same as bicantitruncated tesseractic honeycomb)
[97] CDel nodes 01.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,1,3,4{31,1,3,4}
(Same as runcicantellated tesseractic honeycomb)
[95] CDel nodes 01.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,2,3,4{31,1,3,4}
(Same as runcitruncated tesseractic honeycomb)
[100] CDel nodes 01.pngCDel split2.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
t0,1,2,3,4{31,1,3,4}
(Same as runcicantitruncated tesseractic honeycomb)

F~4 [3,4,3,3] family[edit]

There are 32 honeycombs in this family, 31 reflective forms and one snub.[3] They are named as truncated forms from the regular 16-cell honeycomb and 24-cell honeycomb. These 31 forms are listed by the regular generators in two groups of 19, with 7 shared between.

From the regular 24-cell honeycomb, 19 forms are:

# Coxeter-Dynkin
andSchläfli
symbols
Name Facets by location: [3,4,3,3]
4 3 2 1 0
CDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
[3,4,3]
CDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel 2.pngCDel node.png
[3,4]×[ ]
CDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png
[3]×[3]
CDel node.pngCDel 2.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
[ ]×[3,3]
CDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
[4,3,3]
104 CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
{3,4,3,3}
24-cell honeycomb {3,4,3} - - - -
[93] CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1{3,4,3,3}
Rectified 24-cell honeycomb t1{3,4,3} - - - {4,3,3}
106 CDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t2{3,4,3,3}
Birectified 24-cell honeycomb t1{3,4,3} - - - t1{4,3,3}
106 CDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t2{3,4,3,3}
Birectified 24-cell honeycomb
105 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1{3,4,3,3}
Truncated 24-cell honeycomb
107 CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t1,2{3,4,3,3}
Bitruncated 24-cell honeycomb
? CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,2{3,4,3,3}
Cantellated 24-cell honeycomb
116 CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,3{3,4,3,3}
Bicantellated 24-cell honeycomb
122 CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,3{3,4,3,3}
Runcinated 24-cell honeycomb
121 CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,4{3,4,3,3}
Stericated 24-cell honeycomb
[99] CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,2{3,4,3,3}
Cantitruncated 24-cell honeycomb
119 CDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,3{3,4,3,3}
Bicantitruncated 24-cell honeycomb
128 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,3{3,4,3,3}
Runcitruncated 24-cell honeycomb
125 CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,2,3{3,4,3,3}
Runcicantellated 24-cell honeycomb
127 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,4{3,4,3,3}
Steritruncated 24-cell honeycomb
124 CDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,4{3,4,3,3}
Stericantellated 24-cell honeycomb
131 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,2,3{3,4,3,3}
Runcicantitruncated 24-cell honeycomb
130 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,2,4{3,4,3,3}
Stericantitruncated 24-cell honeycomb
129 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3,4{3,4,3,3}
Steriruncitruncated 24-cell honeycomb
132 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,3,4{3,4,3,3}
Omnitruncated 24-cell honeycomb
[133] CDel node h.pngCDel 3.pngCDel node h.pngCDel 3.pngCDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,2{3,3,4,3}
Snub 24-cell honeycomb

From the regular 16-cell honeycomb, 19 forms are:

# Coxeter-Dynkin
andSchläfli
symbols
Name Facets by location: [3,3,4,3]
4 3 2 1 0
CDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
[3,3,4]
CDel node.pngCDel 2.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
[3,3]×[ ]
CDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png
[3]×[3]
CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel 2.pngCDel node.png
[ ]×[4,3]
CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.png
[3,4,3]
88 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
t0{3,3,4,3}
16-cell honeycomb
[104] CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
t1{3,3,4,3}
Rectified 16-cell honeycomb t1{3,3,4} - - - {3,4,3}
[106] CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
t2{3,3,4,3}
Birectified 16-cell honeycomb
[99] CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
t0,1{3,3,4,3}
Truncated 16-cell honeycomb
113 CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
t1,2{3,3,4,3}
Bitruncated 16-cell honeycomb
112 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
t0,2{3,3,4,3}
Cantellated 16-cell honeycomb
[116] CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,3{3,3,4,3}
Bicantellated 16-cell honeycomb
115 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,3{3,3,4,3}
Runcinated 16-cell honeycomb
[121] CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,4{3,3,4,3}
Stericated 16-cell honeycomb
114 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.png
t0,1,2{3,3,4,3}
Cantitruncated 16-cell honeycomb
[119] CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png
t1,2,3{3,3,4,3}
Bicantitruncated 16-cell honeycomb
117 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,3{3,3,4,3}
Runcitruncated 16-cell honeycomb
118 CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,2,3{3,3,4,3}
Runcicantellated 16-cell honeycomb
123 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,4{3,3,4,3}
Steritruncated 16-cell honeycomb
[124] CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,2,4{3,3,4,3}
Stericantellated 16-cell honeycomb
120 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.png
t0,1,2,3{3,3,4,3}
Runcicantitruncated 16-cell honeycomb
126 CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png
t0,1,2,4{3,3,4,3}
Stericantitruncated 16-cell honeycomb
[129] CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,3,4{3,3,4,3}
Steriruncitruncated 16-cell honeycomb
[132] CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.png
t0,1,2,3,4{3,3,4,3}
Omnitruncated 16-cell honeycomb
[133] CDel node h.pngCDel 3.pngCDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
t0,1{3,4,3,3}
Snub 24-cell honeycomb

A~4 [3[5]] family[edit]

There are 7 honeycombs in this family,[4] all unique to this family, all given below.

# Coxeter-Dynkin
andSchläfli
symbols
Name Facets by location
4 3 2 1 0
CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
[3,3,3]
CDel node.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
[ ]x[3,3]
CDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 3.pngCDel node.png
[3]x[3]
CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.png
[3,3]x[ ]
CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
[3,3,3]
134 CDel node 1.pngCDel split1.pngCDel nodes.pngCDel 3ab.pngCDel branch.png
{3[5]}
5-cell honeycomb
135 CDel node 1.pngCDel split1.pngCDel nodes 10lur.pngCDel 3ab.pngCDel branch.png
t0,1{3[5]}
Truncated 5-cell honeycomb
136 CDel node 1.pngCDel split1.pngCDel nodes.pngCDel 3ab.pngCDel branch 10l.png
t0,2{3[5]}
Cantellated 5-cell honeycomb
137 CDel node 1.pngCDel split1.pngCDel nodes 10lur.pngCDel 3ab.pngCDel branch 10l.png
t0,1,2{3[5]}
Cantitruncated 5-cell honeycomb
138 CDel node 1.pngCDel split1.pngCDel nodes 10lur.pngCDel 3ab.pngCDel branch 01l.png
t0,1,3{3[5]}
Runcitruncated 5-cell honeycomb
139 CDel node 1.pngCDel split1.pngCDel nodes 10lur.pngCDel 3ab.pngCDel branch 11.png
t0,1,2,3{3[5]}
Runcicantitruncated 5-cell honeycomb
140 CDel node 1.pngCDel split1.pngCDel nodes 11.pngCDel 3ab.pngCDel branch 11.png
t0,1,2,3,4{3[5]}
Omnitruncated 5-cell honeycomb

D~4 [31,1,1,1] family[edit]

There are 9 honeycombs in this family,[5] all repeated, with all 9 forms given below.

# Coxeter-Dynkin
andSchläfli
symbols
Name Facets by location: [3,4,3,3]
4 3 2 1 0
CDel nodes.pngCDel 2.pngCDel nodes.png CDel node.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes.png CDel node.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes.png CDel node.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes.png CDel node.pngCDel 3.pngCDel node.pngCDel split1.pngCDel nodes.png
[?] CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel split1.pngCDel nodes.png
{31,1,1,1}
-
[104] CDel nodes.pngCDel split2.pngCDel node 1.pngCDel split1.pngCDel nodes.png
t4{31,1,1,1}
Same as 24-cell honeycomb - t1{31,1,1}

Schlegel wireframe 24-cell.png

t1{31,1,1}

Schlegel wireframe 24-cell.png

t1{31,1,1}

Schlegel wireframe 24-cell.png

t1{31,1,1}

Schlegel wireframe 24-cell.png

[?] CDel nodes.pngCDel split2.pngCDel node 1.pngCDel split1.pngCDel nodes.png
t0,4{31,1,1,1}
-
[?] CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel split1.pngCDel nodes 10l.png
t0,1{31,1,1,1}
-
[?] CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel split1.pngCDel nodes 10l.png
t0,1,4{31,1,1,1}
-
[?] CDel nodes 10ru.pngCDel split2.pngCDel node.pngCDel split1.pngCDel nodes 11.png
t0,1,2{31,1,1,1}
-
[?] CDel nodes 10ru.pngCDel split2.pngCDel node 1.pngCDel split1.pngCDel nodes 11.png
t0,1,4{31,1,1,1}
-
[?] CDel nodes 11.pngCDel split2.pngCDel node.pngCDel split1.pngCDel nodes 11.png
t0,1,2,3{31,1,1,1}
{}x{}x{}x{}
Schlegel wireframe 8-cell.png
t0,2,3{31,1,1}

Schlegel half-solid cantellated 16-cell.png

t0,2,3{31,1,1}

Schlegel half-solid cantellated 16-cell.png

t0,2,3{31,1,1}

Schlegel half-solid cantellated 16-cell.png

t0,2,3{31,1,1}

Schlegel half-solid cantellated 16-cell.png

[?] CDel nodes 11.pngCDel split2.pngCDel node 1.pngCDel split1.pngCDel nodes 11.png
t0,1,2,3,4{31,1,1,1}
{}x{}x{}x{}
Schlegel wireframe 8-cell.png
t0,1,2,3{31,1,1}

Schlegel half-solid truncated 24-cell.png

t0,1,2,3{31,1,1}

Schlegel half-solid truncated 24-cell.png

t0,1,2,3{31,1,1}

Schlegel half-solid truncated 24-cell.png

t0,1,2,3{31,1,1}

Schlegel half-solid truncated 24-cell.png

Duoprismatic forms[edit]

Coxeter groups:

  • B~2xB~2: [4,4]x[4,4] CDel node.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.png
  • B~2xH~2: [4,4]x[6,3] CDel node.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png
  • H~2xH~2: [6,3]x[6,3] CDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png

[4,4]×[4,4][edit]

There are 15 reflective combinatoric forms, but only 3 unique ones.

# Coxeter-Dynkin
andSchläfli
symbols
Name
1 CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.png
[1] CDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.png
6 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.png
[1] CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.png
[6] CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.png
[1] CDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.png
[6] CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.png
[1] CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.png
[6] CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.png
63 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.png
[6] CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.png
[63] CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.png
[1] CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.png
[6] CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.png
[63] CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.png
10 CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.png
[10] CDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.png
67 CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.png
[10] CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.png
[67] CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.png

[4,4]x[6,3][edit]

There are 35 reflective combinatoric forms.

# Coxeter-Dynkin Name
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png
CDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png
CDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node h.pngCDel 4.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png

[6,3]x[6,3][edit]

There are 28 reflective combinatoric forms.

# Coxeter-Dynkin diagram Name
CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.png
CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png
CDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node 1.pngCDel 3.pngCDel node 1.png

References[edit]

  1. ^ George Olshevsky (2006), Uniform Panoploid Tetracombs, manuscript. Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs.
  2. ^ Olshevsky section V
  3. ^ Olshevsky section VI
  4. ^ Olshevsky section VII
  5. ^ Olshevsky section VII

External links[edit]