Sphenoverted trisicositetrachoron
Sphenoverted trisicositetrachoron | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Wavaty |
Coxeter diagram | o3x4o3x4/3*b () |
Elements | |
Cells | 24 cuboctahedra, 24 quasitruncated hexahedra, 24 great cubicuboctahedra |
Faces | 96+192 triangles, 144 squares, 144 octagrams |
Edges | 288+576 |
Vertices | 288 |
Vertex figure | Wedge, edge lengths 1 (2 base edges and top edge), √2 (remaining base edges), and √2–√2 (side edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Gocco–8/3–quith: 135° |
Co–3–quith: 120° | |
Gocco–3–gocco: 120° | |
Gocco–4–co: 45° | |
Related polytopes | |
Army | Srico, edge length |
Regiment | Wavaty |
Conjugate | Retrosphenoverted trisicositetrachoron |
Convex core | Icositetrachoron |
Abstract & topological properties | |
Flag count | 10368 |
Euler characteristic | –72 |
Orientable | Yes |
Properties | |
Symmetry | F4, order 1152 |
Convex | No |
Nature | Tame |
The sphenoverted trisicositetrachoron, or wavaty, is a nonconvex uniform polychoron that consists of 24 cuboctahedra, 24 quasitruncated hexahedra, and 24 great cubicuboctahedra. 1 cuboctahedron, 2 quasitruncated hexahedra, and 2 great cubicuboctahedra join at each vertex.
The sphenoverted trisicositetrachoron contains the vertices of a quasiprismatorhombated hexadecachoron.
Vertex coordinates[edit | edit source]
The vertices of a sphenoverted trisicositetrachoron of edge length 1 are given by all permutations of:
The second set of vertices are identical to those of an inscribed quasiprismatorhombated hexadecachoron.
The polychoron in dual F4 symmetry has vertex coordinates given by all permutations of:
Related polychora[edit | edit source]
The sphenoverted trisicositetrachoron is the colonel of a 7-member regiment. Its other members include the quasirhombated icositetrachoron, great rhombic disicositetrachoron, great pseudorhombic disicositetrachoron, grand quasirhombic disicositetrachoron, prismatoicositetrintercepted disicositetrachoron, and icositetrintercepted trisicositetrachoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 6: Sphenoverts" (#228).
- Klitzing, Richard. "wavaty".