# Octagonal-square coil

Octagonal-square coil
Rank2
Dimension4
TypeRegular
Notation
Schläfli symbol${\displaystyle \{8\}\#\{4\}}$
${\displaystyle \left\{{\dfrac {8}{1,2}}\right\}}$
Elements
Edges8
Vertices8
Related polytopes
Army8-2 step prism
DualOctagonal-square coil
Abstract & topological properties
Flag count16
Euler characteristic0
Schläfli type{8}
OrientableYes
Properties
Symmetry8-2 step prismatic symmetry, order 16
ConvexNo
Dimension vector(2,2)

The octagonal-square coil is a regular skew polygon in 4-dimensional Euclidean space. It is the blend of an octagon and a square. It consists of a set of 8 edges from the 8-2 step prism.

## Vertex coordinates

Its vertex coordinates are the same as those of the 8-2 step prism.

## Related polytopes

### Other skew octagons

The octagonal-square coil is one of 12 regular octagons in Euclidean space:

Octagons in Euclidean space
Name Extended Schläfli symbol Dimensions
octagon ${\displaystyle \left\{{\dfrac {8}{1}}\right\}}$ 2
octagram ${\displaystyle \left\{{\dfrac {8}{3}}\right\}}$ 2
octagonal-square coil ${\displaystyle \left\{{\dfrac {8}{1,2}}\right\}}$ 4
octagonal-octagrammic coil ${\displaystyle \left\{{\dfrac {8}{1,3}}\right\}}$ 4
skew octagon ${\displaystyle \left\{{\dfrac {8}{1,4}}\right\}}$ 3
square-octagrammic coil ${\displaystyle \left\{{\dfrac {8}{2,3}}\right\}}$ 4
skew octagram ${\displaystyle \left\{{\dfrac {8}{3,4}}\right\}}$ 3
octagonal-square-octagrammic coil ${\displaystyle \left\{{\dfrac {8}{1,2,3}}\right\}}$ 6
skew octagonal-square coil ${\displaystyle \left\{{\dfrac {8}{1,2,4}}\right\}}$ 5
skew octagonal-octagrammic coil ${\displaystyle \left\{{\dfrac {8}{1,3,4}}\right\}}$ 5
skew square-octagrammic coil ${\displaystyle \left\{{\dfrac {8}{2,3,4}}\right\}}$ 5
skew octagonal-square-octagrammic coil ${\displaystyle \left\{{\dfrac {8}{1,2,3,4}}\right\}}$ 7