# ❴4,8∣3❵

{4,8∣3}
Rank3
Dimension4
TypeRegular
Notation
Schläfli symbol{4,8∣3}
Elements
Faces288 squares
Edges576
Vertices144
Vertex figureSkew octagon, edge length ${\sqrt {2}}$ HolesTriangles
Measures (edge length 1)
Circumradius${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$ Related polytopes
ArmySpic
RegimentSpic
Dual{8,4∣3}
Petrie dualPetrial ❴4,8∣3❵
φ 3 {8,8/3∣3}
Conjugates{4,8/3∣3}
Abstract & topological properties
Flag count2304
Euler characteristic-144
Schläfli type{4,8}
OrientableYes
Genus73
Properties
SymmetryF4×2, order 2304
ConvexNo
Dimension vector(3,2,3) Relations between polyhedra with planar faces and F4×2 symmetry. δ {\displaystyle \delta } represents the dual, ϕ 3 {\displaystyle \phi _{3}} represents third-order facetting, and c {\displaystyle c} represents the conjugate.

{4,8∣3} is a regular skew polyhedron in 4-space. Its faces are precisely the square faces of the small prismatotetracontoctachoron, and it contains both cubic and octahedral pseudocells. It can be third-order facetted to form the regular skew polyhedron {8,8/3∣3}.

## Vertex coordinates

Its vertex coordinates are the same as those of the small prismatotetracontoctachoron.