Decagonal-decagrammic coil

Decagonal-decagrammic coil
Rank	2
Dimension	4
Notation
Schläfli symbol	$\{10\}\#\{10/3\}$, $\left\{{\frac {10}{1,3}}\right\}$
Elements
Edges	10
Vertices	10
Vertex figure	Dyad
Related polytopes
Army	10-3 step prism
Dual	Decagonal-decagrammic coil
Convex hull	10-3 step prism
Abstract & topological properties
Flag count	20
Euler characteristic	0
Schläfli type	{10}
Orientable	Yes
Properties
Symmetry	10-3 step prismatic symmetry, order 20
Convex	No
Dimension vector	(2,2)

The decagonal-decagrammic coil is a regular skew polygon in 4-dimensional Euclidean space. It can be constructed by blending the decagon $\left\{{\frac {10}{1}}\right\}$ and the decagram $\left\{{\frac {10}{3}}\right\}$, so the decagonal-decagrammic coil has the Schläfli symbol $\left\{{\frac {10}{1,3}}\right\}$.

The decagonal-decagrammic coil appears as the Petrie polygon of the skew pure dodecahedron.

It has 10 edges that form a subset of those of the 10-3 step prism, a variant of the bidecachoron.

Vertex coordinates

Its vertex coordinates are the same as those found in the bidecachoron, and more generally any 10-3 step prism.