# Decagonal-decagrammic coil

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Decagonal-decagrammic coil
Rank2
Dimension4
Notation
Schläfli symbol${\displaystyle \{10\}\#\{10/3\}}$, ${\displaystyle \left\{{\frac {10}{1,3}}\right\}}$
Elements
Edges10
Vertices10
Vertex figureDyad
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 ${\displaystyle \left\{{\frac {10}{1}}\right\}}$ and the decagram ${\displaystyle \left\{{\frac {10}{3}}\right\}}$, so the decagonal-decagrammic coil has the Schläfli symbol ${\displaystyle \left\{{\frac {10}{1,3}}\right\}}$.

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.