Apeir hemidodecahedron (4-dimensional)

Apeir hemidodecahedron (4-dimensional)
Rank	4
Dimension	4
Elements
Cells	6 apeir pentagonal-pentagrammic coils
Faces	∞ zigzags
Edges	∞
Vertices	∞
Vertex figure	4-dimensional hemidodecahedron
Related polytopes
Petrie dual	Apeir hemidodecahedron (4-dimensional)
Abstract & topological properties
Schläfli type	{∞,5,3}
Orientable	No
Properties
Flag orbits	1
Convex	No
Dimension vector	(0,2,2,2)

The apeir hemidodecahedron is a regular apeirochoron in 4-dimensional space. It is the apeir of the 4-dimensional hemidodecahedron. Since the 4-dimensional hemidodecahedron has a rational coordinate represenation its apeir is discrete.

It is self-Petrial.

Vertex coordinates

Simple vertex coordinates can be given in 5 dimensions as sums of permutations of:

• $\left(-3,\,-3,\,2,\,2,\,2\right)$