Hexagonal-triangular coil

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Hexagonal-triangular coil
Schläfli symbol,
Vertex figureDyad
Related polytopes
DualHexagonal-triangular coil
Convex hull6-2 step prism
Abstract & topological properties
Flag count12
Euler characteristic0
Schläfli type{6}
Symmetry6-2 step prismatic symmetry
Dimension vector(2,2)

The hexagonal-triangular coil is a regular skew polygon in 4-dimensional Euclidean space, which can be obtained by blending a hexagon and a triangle (). It is one of five regular hexagons in Euclidean space.

Its edges form a subset of 6 edges of a 6-2 step prism, which is a variant of the more symmetrical triangular duotegum.

Vertex coordinates[edit | edit source]

The vertex coordinates of the hexagonal-triangular coil are the same as those found in a 6-2 step prism.

Related polytopes[edit | edit source]

The hexagonal-triangular coil is the second-smallest possible regular skew polygon in 4D Euclidean space, the smallest being the 5-sided pentagonal-pentagrammic coil.

It is appears as the face of and , which are both 4-dimensional skew polyhedra.

Other skew hexagons[edit | edit source]

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

Hexagons in Euclidean space
Name Extended Schläfli symbol Dimensions
hexagon 2
hexagonal-triangular coil 4
skew hexagon 3
skew triangle 3
skew hexagonal-triangular coil 5