Augmented dodecahedron (Johnson solid)

From Polytope Wiki
Jump to navigation Jump to search
Augmented dodecahedron (Johnson solid)
Rank3
TypeCRF
Notation
Bowers style acronymAud
Coxeter diagramoxfoo ooofx&#xt
Stewart notationJ58
Elements
Faces5 triangles, 1+5+5 pentagons
Edges5+5+5+5+5+10
Vertices1+5+5+5+5
Vertex figures1 pentagon, edge length 1
 5 kites, edge lengths 1 and (1+5)/2
 5+5+5 triangles, edge lengths (1+5)/2
Measures (edge length 1)
Volume
Dihedral angles3–5:
 3–3:
 5–5:
Central density1
Number of external pieces16
Level of complexity14
Related polytopes
ArmyAud
RegimentAud
DualMonotruncated icosahedron
ConjugateMonoexcavated great stellated dodecahedron
Abstract & topological properties
Flag count140
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH2×I, order 10
ConvexYes
NatureTame

The augmented dodecahedron is one of the 92 Johnson solids (J58). It consists of 5 triangles and 1+5+5 pentagons. It can be constructed by attaching a pentagonal pyramid to one of the faces of the regular dodecahedron.

Vertex coordinates[edit | edit source]

An augmented dodecahedron of edge length 1 has vertices given by all even permutations of:

  • ,

As well as:

  • ,
  • .

External links[edit | edit source]