Augmented truncated dodecahedron

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Augmented truncated dodecahedron
Rank3
TypeCRF
Notation
Bowers style acronymAutid
Elements
Faces
Edges5+5+5+5+5+5+5+5+5+10+10+10+10+10+10
Vertices5+5+5+5+5+10+10+10+10
Vertex figures5 isosceles trapezoids, edge length 1, 2, (1+5)/2, 2
 10 irregular tetragons, edge length 1, 2, 1, (5+5)/2
 50 isosceles triangles, edge lengths 1, 2+2, 2+2
Measures (edge length 1)
Volume
Dihedral angles3–4 join:
 3–4 cupolaic:
 3–10 join:
 4–5:
 3–10 tid:
 10–10:
Central density1
Number of external pieces42
Level of complexity42
Related polytopes
ArmyAutid
RegimentAutid
DualRhombirhombistellated triakis icosahedron
ConjugateAugmented quasitruncated great stellated dodecahedron
Abstract & topological properties
Flag count420
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH2×I, order 10
Flag orbits42
ConvexYes
NatureTame

The augmented truncated dodecahedron (OBSA: autid) is one of the 92 Johnson solids (J68). It consists of 5+5+5+5+5 triangles, 5 squares, 1 pentagon, and 1+5+5 decagons. It can be constructed by attaching a pentagonal cupola to one of the decagonal faces of the truncated dodecahedron.

Vertex coordinates[edit | edit source]

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

  • ,
  • ,
  • ,

plus the following additional vertices:

  • ,
  • ,
  • .

External links[edit | edit source]