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 | Tessellation | Vertex figure | Facets per vertex figure | Vertices per vertex figure | Edge figure | |
---|---|---|---|---|---|---|
1 |
Apeirogon |
1 | 2 | |||
2 |
Triangular tiling 2-simplex honeycomb |
Hexagon (Truncated triangle) |
3
triangles 3 rectified triangles |
6 |
Segment | |
3 |
Tetrahedral-octahedral honeycomb 3-simplex honeycomb |
Cuboctahedron (Cantellated tetrahedron) |
4+4
tetrahedron 6 rectified tetrahedron |
12 |
Rectangle | |
4 |
4-simplex honeycomb |
Runcinated 5-cell |
5+5
5-cells 10+10 Rectified 5-cells |
20 |
Triangular antiprism | |
5 |
5-simplex honeycomb |
Stericated 5-simplex |
6+6
5-simplex 15+15 rectified 5-simplex 20 birectified 5-simplex |
30 |
Tetrahedral antiprism | |
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 | 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 | 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 | 9-simplex honeycomb |
100 | 7-simplex antiprism | |||
10 | 10-simplex 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 | Tessellation | Vertex figure | Facets per vertex figure | Vertices per vertex figure | Edge figure | |
---|---|---|---|---|---|---|
1 |
Apeirogon |
1 | 2 | |||
2 |
Triangular tiling 2-simplex honeycomb |
Hexagon (Truncated triangle) |
3
triangles 3 rectified triangles |
6 |
Segment | |
3 |
Tetrahedral-octahedral honeycomb 3-simplex honeycomb |
Cuboctahedron (Cantellated tetrahedron) |
4+4
tetrahedron 6 rectified tetrahedron |
12 |
Rectangle | |
4 |
4-simplex honeycomb |
Runcinated 5-cell |
5+5
5-cells 10+10 Rectified 5-cells |
20 |
Triangular antiprism | |
5 |
5-simplex honeycomb |
Stericated 5-simplex |
6+6
5-simplex 15+15 rectified 5-simplex 20 birectified 5-simplex |
30 |
Tetrahedral antiprism | |
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 | 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 | 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 | 9-simplex honeycomb |
100 | 7-simplex antiprism | |||
10 | 10-simplex honeycomb | ... | ... |