❴4,8∣3❵

{4,8∣3}
Rank	3
Dimension	4
Type	Regular
Notation
Schläfli symbol	{4,8∣3}
Elements
Faces	288 squares
Edges	576
Vertices	144
Vertex figure	Skew octagon, edge length ${\sqrt {2}}$
Holes	Triangles
Measures (edge length 1)
Circumradius	${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Related polytopes
Army	Spic
Regiment	Spic
Dual	{8,4∣3}
Petrie dual	Petrial ❴4,8∣3❵
φ 3	{8,8/3∣3}
Conjugates	{4,8/3∣3}
Abstract & topological properties
Flag count	2304
Euler characteristic	-144
Schläfli type	{4,8}
Orientable	Yes
Genus	73
Properties
Symmetry	F4×2, order 2304
Convex	No
Dimension vector	(3,2,3)

Relations between polyhedra with planar faces and F₄×2 symmetry. $\delta$ represents the dual, $\phi _{3}$ represents third-order facetting, and $c$ 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.