Skew hexagonal-triangular coil

Skew hexagonal-triangular coil
Rank	2
Dimension	5
Type	Regular
Notation
Schläfli symbol	$\{6\}\#\{3\}\#\{\}$ $\left\{{\dfrac {6}{1,2,3}}\right\}$
Elements
Edges	6
Vertices	6
Vertex figure	Dyad
Related polytopes
Dual	Hexagonal-triangular coil
Abstract & topological properties
Flag count	12
Euler characteristic	0
Schläfli type	{6}
Orientable	Yes
Properties
Convex	No
Dimension vector	(2,3)

The skew hexagonal-triangular coil is a regular skew polygon in 5-dimensional Euclidean space, which can be obtained by blending a hexagon, a triangle and a dyad ($\{6\}\#\{3\}\#\{\}$). It is one of five regular hexagons in Euclidean space.

Related polytopes

The skew hexagonal-triangular coil is the smallest possible regular skew polygon in 5D Euclidean space.

It is the Petrie polygon of the 5-simplex.

Other skew hexagons

The skew hexagonal-triangular coil is one of five regular hexagons in Euclidean space:

Hexagons in Euclidean space

Name	Extended Schläfli symbol	Dimensions
hexagon	$\left\{{\dfrac {6}{1}}\right\}$	2
hexagonal-triangular coil	$\left\{{\dfrac {6}{1,2}}\right\}$	4
skew hexagon	$\left\{{\dfrac {6}{1,3}}\right\}$	3
skew triangle	$\left\{{\dfrac {6}{2,3}}\right\}$	3
skew hexagonal-triangular coil	$\left\{{\dfrac {6}{1,2,3}}\right\}$	5