Skew pure dodecahedron

Skew pure dodecahedron
Rank	3
Dimension	4
Type	Regular
Notation
Schläfli symbol	$\left\{{\frac {5}{1,2}},3:{\frac {10}{1,3}}\right\}$
Elements
Faces	12 pentagonal-pentagrammic coils
Edges	30
Vertices	20
Vertex figure	Triangle
Petrie polygons	6 decagonal-decagrammic coils $\left\{{\dfrac {10}{1,3}}\right\}$
Related polytopes
Army	Bamid
Petrie dual	Petrial skew pure dodecahedron
Abstract & topological properties
Flag count	120
Euler characteristic	2
Schläfli type	{5,3}
Orientable	Yes
Properties
Convex	No
Dimension vector	(2,2,2)

For the dodecahedron blended with a digon, see Blended dodecahedron.

The skew pure dodecahedron is a regular skew polyhedron in 4-dimensional Euclidean space. It is abstractly equivalent to the regular dodecahedron in 3-dimensional Euclidean space. It is pure, so even though it is a skew embedding of the dodecahedron it can not be decomposed into the blend of two other polyhedra.

Vertex coordinates

The vertex coordinates of the skew pure dodecahedron with an edge length of 1 are the same as those of the biambodecachoron, where the 30 smaller edges are sized to be length 1.

External links

• Hartley, Michael. "{5,3}*120".