# Decagonal-decagrammic coil

Decagonal-decagrammic coil
Rank2
Dimension4
Notation
Schläfli symbol$\{10\}\#\{10/3\}$ , $\left\{{\frac {10}{1,3}}\right\}$ Elements
Edges10
Vertices10
Related polytopes
Army10-3 step prism
DualDecagonal-decagrammic coil
Convex hull10-3 step prism
Abstract & topological properties
Flag count20
Euler characteristic0
Schläfli type{10}
OrientableYes
Properties
Symmetry10-3 step prismatic symmetry, order 20
ConvexNo
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.