Dodecahedron (6-dimensional)

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Dodecahedron (6-dimensional)
Rank3
Dimension6
TypeRegular
Notation
Schläfli symbol{5,3}#{5/2,3}
Elements
Faces12 pentagonal-pentagrammic coils
Edges30
Vertices20
Vertex figureTriangle
Petrie polygons6 skew decagonal-decagrammic coils
Related polytopes
DualSkew icosahedron
Petrie dualPetrial dodecahedron (6-dimensional)
ConjugateDodecahedron (6-dimensional)
Convex hullDodecahedral-great stellated dodecahedral step prism
Abstract & topological properties
Flag count120
Euler characteristic2
Schläfli type{5,3}
OrientableYes
Genus0
SkeletonDodecahedral graph
Properties
ConvexNo
Dimension vector(4,4,4)

The blend of the dodecahedron and the great stellated dodecahedron is a regular skew polyhedron in 6 dimensions. It is abstractly equivalent to the dodecahedron, and is the unique faithful symmetric realization of {5,3} in 6-dimensions.

Related polytopes[edit | edit source]

The blend of the dodecahedron and the great stellated dodecahedron is on of 28 faithful symmetric realizations of the abstract regular polytope {5,3}.

Faithful symmetric realizations of {5,3}
Dimension Components Name
3 Dodecahedron Dodecahedron
3 Great stellated dodecahedron Great stellated dodecahedron
4 Skew pure dodecahedron Skew pure dodecahedron
6 Dodecahedron
Great stellated dodecahedron
Dodecahedron (6-dimensional)
7 Dodecahedron
Skew pure dodecahedron
7 Great stellated dodecahedron
Skew pure dodecahedron
7 Dodecahedron
Hemidodecahedron (4-dimensional)
7 Great stellated dodecahedron
Hemidodecahedron (4-dimensional)
8 Dodecahedron
Hemidodecahedron (5-dimensional)
8 Great stellated dodecahedron
Hemidodecahedron (5-dimensional)
8 Skew pure dodecahedron
Hemidodecahedron (4-dimensional)
10 Dodecahedron
Great stellated dodecahedron
Skew pure dodecahedron
Dodecahedron (cross-polytope realization)
10 Dodecahedron
Great stellated dodecahedron
Hemidodecahedron (4-dimensional)
11 Dodecahedron
Skew pure dodecahedron
Hemidodecahedron (4-dimensional)
11 Great stellated dodecahedron
Skew pure dodecahedron
Hemidodecahedron (4-dimensional)
11 Dodecahedron
Great stellated dodecahedron
Hemidodecahedron (5-dimensional)
12 Dodecahedron
Skew pure dodecahedron
Hemidodecahedron (5-dimensional)
12 Great stellated dodecahedron
Skew pure dodecahedron
Hemidodecahedron (5-dimensional)
12 Dodecahedron
Hemidodecahedron (4-dimensional)
Hemidodecahedron (5-dimensional)
12 Great stellated dodecahedron
Hemidodecahedron (4-dimensional)
Hemidodecahedron (5-dimensional)
13 Skew pure dodecahedron
Hemidodecahedron (4-dimensional)
Hemidodecahedron (5-dimensional)
14 Dodecahedron
Great stellated dodecahedron
Skew pure dodecahedron
Hemidodecahedron (4-dimensional)
15 Dodecahedron
Great stellated dodecahedron
Hemidodecahedron (4-dimensional)
Hemidodecahedron (5-dimensional)
15 Dodecahedron
Great stellated dodecahedron
Skew pure dodecahedron
Hemidodecahedron (5-dimensional)
16 Dodecahedron
Skew pure dodecahedron
Hemidodecahedron (4-dimensional)
Hemidodecahedron (5-dimensional)
16 Great stellated dodecahedron
Skew pure dodecahedron
Hemidodecahedron (4-dimensional)
Hemidodecahedron (5-dimensional)
19 Dodecahedron
Great stellated dodecahedron
Skew pure dodecahedron
Hemidodecahedron (4-dimensional)
Hemidodecahedron (5-dimensional)

External links[edit | edit source]