User:Tomruen/Simplectic honeycomb

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In geometry a simplectic honeycomb or k-simplex honeycomb is one of a dimensional set of uniform tessellations. Each is composed of simplex facets, or various rectifications of them. The vertex figure for each is an expanded simplex.

n {\tilde{A}}_{2+} Tessellation Vertex figure Facets per vertex figure Vertices per vertex figure Edge figure
1 {\tilde{A}}_1 Regular apeirogon.png
Apeirogon
CDel node 1.pngCDel infin.pngCDel node.png
CDel node 1.png 1 2
2 {\tilde{A}}_2 Uniform tiling 333-t1.png
Triangular tiling
2-simplex honeycomb
CDel node 1.pngCDel split1.pngCDel branch.png
Truncated triangle.png
Hexagon
(Truncated triangle)
CDel node 1.pngCDel 3.pngCDel node 1.png
3 triangles
3 rectified triangles
6 Segment
CDel node 1.png
3 {\tilde{A}}_3 Tetrahedral-octahedral honeycomb.png
Tetrahedral-octahedral honeycomb
3-simplex honeycomb
CDel node 1.pngCDel split1.pngCDel nodes.pngCDel split2.pngCDel node.png
Uniform polyhedron-33-t02.png
Cuboctahedron
(Cantellated tetrahedron)
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
4+4 tetrahedron
6 rectified tetrahedron
12 Rectangle
CDel node 1.pngCDel 2.pngCDel node 1.png
4 {\tilde{A}}_4 4-simplex honeycomb
CDel node 1.pngCDel split1.pngCDel nodes.pngCDel 3ab.pngCDel branch.png
Schlegel half-solid runcinated 5-cell.png
Runcinated 5-cell
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5+5 5-cells
10+10 Rectified 5-cells
20 Runcinated 5-cell verf.png
Triangular antiprism
CDel node h.pngCDel 3.pngCDel node h.pngCDel 2.pngCDel node h.png
5 {\tilde{A}}_5 5-simplex honeycomb
CDel node 1.pngCDel split1.pngCDel nodes.pngCDel 3ab.pngCDel nodes.pngCDel split2.pngCDel node.png
Stericated hexateron ortho.svg
Stericated 5-simplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
6+6 5-simplex
15+15 rectified 5-simplex
20 birectified 5-simplex
30 Stericated hexateron verf.png
Tetrahedral antiprism
CDel node h.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 2.pngCDel node h.png
6 {\tilde{A}}_6 6-simplex honeycomb
CDel node 1.pngCDel split1.pngCDel nodes.pngCDel 3ab.pngCDel nodes.pngCDel 3ab.pngCDel branch.png
Pentellated 6-simplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
7+7 6-simplex
21+21 rectified 6-simplex
35+35 birectified 6-simplex
42 4-simplex antiprism
7 {\tilde{A}}_7 7-simplex honeycomb
CDel node 1.pngCDel split1.pngCDel nodes.pngCDel 3ab.pngCDel nodes.pngCDel 3ab.pngCDel nodes.pngCDel split2.pngCDel node.png
Hexicated 7-simplex
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
8+8 7-simplex
28+28 rectified 7-simplex
56+56 birectified 7-simplex
70 trirectified 7-simplex
56 5-simplex antiprism
8 {\tilde{A}}_8 8-simplex honeycomb
CDel node 1.pngCDel split1.pngCDel nodes.pngCDel 3ab.pngCDel nodes.pngCDel 3ab.pngCDel nodes.pngCDel 3ab.pngCDel branch.png
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png 9+9 8-simplex
36+36 rectified 8-simplex
84+84 birectified 8-simplex
126+126 trirectified 8-simplex
72 6-simplex antiprism
9 {\tilde{A}}_9 9-simplex honeycomb
CDel node 1.pngCDel split1.pngCDel nodes.pngCDel 3ab.pngCDel nodes.pngCDel 3ab.pngCDel nodes.pngCDel 3ab.pngCDel nodes.pngCDel split2.pngCDel node.png
CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png 100 7-simplex antiprism
10 10-simplex honeycomb ... ...