# User:Tomruen/Simplectic honeycomb

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 ${\tilde{A}}_1$
Apeirogon
1 2
2 ${\tilde{A}}_2$
Triangular tiling
2-simplex honeycomb

Hexagon
(Truncated triangle)
3 triangles
3 rectified triangles
6 Segment
3 ${\tilde{A}}_3$
Tetrahedral-octahedral honeycomb
3-simplex honeycomb

Cuboctahedron
(Cantellated tetrahedron)
4+4 tetrahedron
6 rectified tetrahedron
12 Rectangle
4 ${\tilde{A}}_4$ 4-simplex honeycomb

Runcinated 5-cell
5+5 5-cells
10+10 Rectified 5-cells
20
Triangular antiprism
5 ${\tilde{A}}_5$ 5-simplex honeycomb

Stericated 5-simplex
6+6 5-simplex
15+15 rectified 5-simplex
20 birectified 5-simplex
30
Tetrahedral antiprism
6 ${\tilde{A}}_6$ 6-simplex honeycomb
Pentellated 6-simplex
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
Hexicated 7-simplex
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
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
100 7-simplex antiprism
10 10-simplex honeycomb ... ...