Octagonal-square coil

Octagonal-square coil
Rank	2
Dimension	4
Type	Regular
Notation
Schläfli symbol	$\{8\}\#\{4\}$ $\left\{{\dfrac {8}{1,2}}\right\}$
Elements
Edges	8
Vertices	8
Vertex figure	Dyad
Related polytopes
Army	8-2 step prism
Dual	Octagonal-square coil
Abstract & topological properties
Flag count	16
Euler characteristic	0
Schläfli type	{8}
Orientable	Yes
Properties
Symmetry	8-2 step prismatic symmetry, order 16
Convex	No
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	$\left\{{\dfrac {8}{1}}\right\}$	2
octagram	$\left\{{\dfrac {8}{3}}\right\}$	2
octagonal-square coil	$\left\{{\dfrac {8}{1,2}}\right\}$	4
octagonal-octagrammic coil	$\left\{{\dfrac {8}{1,3}}\right\}$	4
skew octagon	$\left\{{\dfrac {8}{1,4}}\right\}$	3
square-octagrammic coil	$\left\{{\dfrac {8}{2,3}}\right\}$	4
skew octagram	$\left\{{\dfrac {8}{3,4}}\right\}$	3
octagonal-square-octagrammic coil	$\left\{{\dfrac {8}{1,2,3}}\right\}$	6
skew octagonal-square coil	$\left\{{\dfrac {8}{1,2,4}}\right\}$	5
skew octagonal-octagrammic coil	$\left\{{\dfrac {8}{1,3,4}}\right\}$	5
skew square-octagrammic coil	$\left\{{\dfrac {8}{2,3,4}}\right\}$	5
skew octagonal-square-octagrammic coil	$\left\{{\dfrac {8}{1,2,3,4}}\right\}$	7