Great hexacosifaceted prismatodishecatonicosachoron

Great hexacosifaceted prismatodishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gix fipady
Elements
Cells	1200 triangular prisms, 120 great stellated dodecahedra, 120 quasirhombicosidodecahedra
Faces	2400 triangles, 3600 squares, 1440 pentagrams
Edges	3600+3600
Vertices	2400
Vertex figure	Triangular hemipodium, edge lengths (√5–1)/2 (top triangle), 1 (base pseudo-triangle), and √2 (sides)
Measures (edge length 1)
Circumradius	$3-\sqrt5 \approx 0.76393$
Dichoral angles	Qrid–5/2–gissid: 72°
	Qrid–4–trip: $\arccos\left(\frac{\sqrt{15}-\sqrt3}{4}\right) ≈ 69.09484°$
	Qrid–3–trip: 30°
Number of external pieces	792120
Level of complexity	3048
Related polytopes
Army	Sidpixhi
Regiment	Gixhihy
Conjugate	Small hexacosifaceted prismatodishecatonicosachoron
Abstract & topological properties
Euler characteristic	1200
Orientable	No
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The great hexacosifaceted prismatodishecatonicosachoron, or gix fipady, is a nonconvex uniform polychoron that consists of 120 quasirhombicosidodecahedra, 120 great stellated dodecahedra, and 1200 triangular prisms. Three quasirhombicosidodecahedra, one great stellated dodecahedra, and three triangular prisms join at each vertex.

It also has 600 tetrahedra and 720 pentagrammic prisms as pseudofacets.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great hexacosihecatonicosihecatonicosachoron.

External links

• Bowers, Jonathan. "Category 12: Podiumverts" (#502).