# Skew hexagonal-triangular coil

Skew hexagonal-triangular coil
Rank2
Dimension5
TypeRegular
Notation
Schläfli symbol${\displaystyle \{6\}\#\{3\}\#\{\}}$
${\displaystyle \left\{{\dfrac {6}{1,2,3}}\right\}}$
Elements
Edges6
Vertices6
Related polytopes
DualHexagonal-triangular coil
Abstract & topological properties
Flag count12
Euler characteristic0
Schläfli type{6}
OrientableYes
Properties
ConvexNo
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 (${\displaystyle \{6\}\#\{3\}\#\{\}}$). 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 ${\displaystyle \left\{{\dfrac {6}{1}}\right\}}$ 2
hexagonal-triangular coil ${\displaystyle \left\{{\dfrac {6}{1,2}}\right\}}$ 4
skew hexagon ${\displaystyle \left\{{\dfrac {6}{1,3}}\right\}}$ 3
skew triangle ${\displaystyle \left\{{\dfrac {6}{2,3}}\right\}}$ 3
skew hexagonal-triangular coil ${\displaystyle \left\{{\dfrac {6}{1,2,3}}\right\}}$ 5