|Bowers style acronym||Bitec|
|Cells||288 tetragonal disphenoids, 576 digonal disphenoids, 48 cubes, 144 square antiprisms|
|Faces||1152+1152 isosceles triangles, 288 squares|
|Vertex figure||Hexakis triangular cupola|
|Measures (based on two truncated icositetrachora of edge length 1)|
|Edge lengths||Edges of truncated icositetrachora (192+576): 1|
|Lacing edges (1152):|
|Abstract & topological properties|
|Symmetry||F4×2, order 2304|
The bitruncatotetracontoctachoron or bitec is a convex isogonal polychoron that consists of 48 cubes, 144 square antiprisms, 288 tetragonal disphenoids, and 576 digonal disphenoids. 1 cube, 3 square antiprisms, 3 tetragonal disphenoids, and 6 digonal disphenoids join at each vertex. It can be obtained as the convex hull of two oppositely oriented truncated icositetrachora.
This polychoron generally has one degree of variation. If the edge length of the truncated icositetrachora are a (those surrounded by truncated octahedra) and b (of cubes), its lacing edges have length and it has circumradius .
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.12786.
Vertex coordinates[edit | edit source]
The vertices of a bitruncatotetracontoctachoron, assuming that the square antiprisms are uniform of edge length 1, centered at the origin, are given by all permutations of:
An alternate set of coordinates, based on two uniform truncated icositetrachora of edge length 1, centered at the origin, are given by all permutations of:
[edit | edit source]
- Klitzing, Richard. "bitec".