Parabiaugmented truncated dodecahedron

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Parabiaugmented truncated dodecahedron
Rank3
TypeCRF
Notation
Bowers style acronymPabautid
Elements
Faces
Edges6×10+3×20
Vertices3×10+20+20
Vertex figures10 isosceles trapezoids, edge length 1, 2, (1+5)/2, 2
 20 irregular tetragons, edge length 1, 2, 1, (5+5)/2
 40 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 pieces52
Level of complexity24
Related polytopes
ArmyPabautid
RegimentPabautid
DualParabirhombirhombistellated triakis icosahedron
ConjugateParabiaugmented quasitruncated great stellated dodecahedron
Abstract & topological properties
Flag count480
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
Symmetry(I2(10)×A1)/2, order 20
Flag orbits24
ConvexYes
NatureTame

The parabiaugmented truncated dodecahedron (OBSA: pabautid) is one of the 92 Johnson solids (J69). It consists of 10+10+10 triangles, 10 squares, 2 pentagons, and 10 decagons. It can be constructed by attaching two pentagonal cupolas to two opposite decagonal faces of the truncated dodecahedron.

Vertex coordinates[edit | edit source]

A parabiaugmented truncated dodecahedron of edge length 1 has vertices given by all even permutations of:

  • ,
  • ,
  • ,

plus the following additional vertices:

  • ,
  • ,
  • .

External links[edit | edit source]