Great stellated tetracontoctachoron

Great stellated tetracontoctachoron
Rank	4
Type	Regular
Notation
Bowers style acronym	Gistic
Elements
Components	6 tesseracts
Cells	48 cubes
Faces	144 squares
Edges	192
Vertices	48
Vertex figure	Stella octangula, edge length √2
Measures (edge length 1)
Circumradius	$1$
Inradius	${\frac {1}{2}}=0.5$
Hypervolume	$6$
Dichoral angle	$90^{\circ }$
Related polytopes
Army	Bicont
Regiment	Stoc
Dual	Small stellated tetracontoctachoron
Conjugate	Great stellated tetracontctachoron
Convex core	Tetracontoctachoron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	No
Nature	Tame

The great stellated tetracontoctachoron or gistic is a regular compound polychoron. It is a compound of six tesseracts. It has 48 cubes as cells, with 8 cells joining at each vertex. It can also be seen as a compound of two great icositetrachora in opposite orientations, formed by replacing each icositetrachoron in the stellated tetracontoctachoron with a great icositetrachoron containing the same vertices and edges.

Like the great icositetrachoron, this compound has fissary vertices, with two components meeting per vertex.

Vertex coordinates

The vertices of a great stellated tetracontoctachoron of edge length 1, centered at the origin, are given by all permutations of:

• $\left(\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {\sqrt {2}}{2}},\,0,\,0\right).$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right),$
• $\left(\pm 1,\,0,\,0,\,0\right).$