Octakis icositetrachoron

Octakis icositetrachoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	m3m4o3o ()
Elements
Cells	192 triangular pyramids
Faces	96 triangles, 288 isosceles triangles
Edges	96+144
Vertices	24+24
Vertex figure	24 octahedra, 24 tetrakis hexahedra
Measures (edge length 1)
Dichoral angle	$\arccos \left(-{\frac {13}{14}}\right)\approx 158.21321^{\circ }$
Central density	1
Related polytopes
Dual	Truncated icositetrachoron
Abstract & topological properties
Flag count	4608
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	Yes
Nature	Tame

The octakis icositetrachoron, also known as the triangular-pyramidal hecatonicenneacontadichoron, is a convex isochoric polychoron with 192 triangular pyramids as cells. It can be obtained as the dual of the truncated icositetrachoron.

It can also be obtained as the convex hull of two dually oriented icositetrachora, where one has edges exactly ${\frac {5{\sqrt {2}}}{6}}\approx 1.17851$ times the length of those of the other. Any convex hull of two dual icositetrachora where one is more than ${\frac {3{\sqrt {2}}}{4}}\approx 1.06066$ times the edge length of the other gives a fully symmetric variant of this polychoron.

Variations

The octakis icositetrachoron has variants that remain isochoric under B₄ symmetry (called the great sphenoidal hecatonenneacontadichoron) and D₄ symmetry (called the tetrahedral hecatonenneacontadichoron).