# Petrial apeir octagonal-octagrammic coil

Petrial apeir octagonal-octagrammic coil
Rank3
Dimension4
TypeRegular
Notation
Schläfli symbol
• {8,8/3}#{8/3,8}
• ${\displaystyle \left\{{\frac {8}{1,3}},{\frac {8}{1,3}}\right\}}$
Elements
FacesOctagonal-octagrammic coils
Edges
Vertices
Vertex figureOctagonal-octagrammic coil
Petrie polygonszigzags
HolesSkew squares
Related polytopes
Dual{8,8/3}#{8/3,8}
Petrie dualApeir octagonal-octagrammic coil
Abstract & topological properties
Schläfli type{8,8}
OrientableYes
Genus
Properties
Flag orbits1
ConvexNo
Dimension vector(2,2,2)

Petrial apeir octagonal-octagrammic coil is a regular skew apeirohedron in 4-dimensional Euclidean space. It is the blend of the order-8 octagrammic tiling with its conjugate the order-8/3 octagonal tiling. It is notable in that it is the blend of two dense polytopes but it is not itself dense.

## Vertex coordinates

Vertex coordinates for a {8,8/3}#{8/3,8} of unit edge length can be given as

• ${\displaystyle \left({\frac {h+i{\sqrt {2}}}{2}},{\frac {h-i{\sqrt {2}}}{2}},{\frac {j+k{\sqrt {2}}}{2}},{\frac {j-k{\sqrt {2}}}{2}}\right)}$,

where h , i , j , and k  are integers.