# Great stellated tetracontoctachoron

Great stellated tetracontoctachoron
Rank4
TypeRegular
Notation
Bowers style acronymGistic
Elements
Components6 tesseracts
Cells48 cubes
Faces144 squares
Edges192
Vertices48
Vertex figureStella octangula, edge length 2
Measures (edge length 1)
Circumradius${\displaystyle 1}$
Inradius${\displaystyle {\frac {1}{2}}=0.5}$
Hypervolume${\displaystyle 6}$
Dichoral angle${\displaystyle 90^{\circ }}$
Related polytopes
ArmyBicont
RegimentStoc
DualSmall stellated tetracontoctachoron
ConjugateGreat stellated tetracontctachoron
Convex coreTetracontoctachoron
Abstract & topological properties
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexNo
NatureTame

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:

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