Sphenoverted trisicositetrachoron

From Polytope Wiki
Jump to navigation Jump to search
Sphenoverted trisicositetrachoron
Rank4
TypeUniform
Notation
Bowers style acronymWavaty
Coxeter diagramo3x4o3x4/3*b ()
Elements
Cells24 cuboctahedra, 24 quasitruncated hexahedra, 24 great cubicuboctahedra
Faces96+192 triangles, 144 squares, 144 octagrams
Edges288+576
Vertices288
Vertex figureWedge, 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 anglesGocco–8/3–quith: 135°
 Co–3–quith: 120°
 Gocco–3–gocco: 120°
 Gocco–4–co: 45°
Related polytopes
ArmySrico, edge length
RegimentWavaty
ConjugateRetrosphenoverted trisicositetrachoron
Convex coreIcositetrachoron
Abstract & topological properties
Flag count10368
Euler characteristic–72
OrientableYes
Properties
SymmetryF4, order 1152
ConvexNo
NatureTame

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]