Paragyrate diminished rhombicosidodecahedron

From Polytope Wiki
Jump to navigation Jump to search
Paragyrate diminished rhombicosidodecahedron
Rank3
TypeCRF
Notation
Bowers style acronymPagydrid
Elements
Faces
Edges7×5+7×10
Vertices5+5+5+4×10
Vertex figures5+30 isosceles trapezoids, edge length 1, 2, (1+5)/2, 2
 10 scalene triangles, edge lengths 2, (1+5)/2, (5+5)/2
 10 irregular tetragons, edge lengths 1, 2, 2, (1+5)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles3–4:
 3–5:
 4–4:
 4–5:
 4–10:
 5–10:
Central density1
Number of external pieces52
Level of complexity42
Related polytopes
ArmyPagydrid
RegimentPagydrid
DualParadeltogyrate stellated deltoidal hexecontahedron
ConjugateParagyrate replenished quasirhombicosidodecahedron
Abstract & topological properties
Flag count420
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH2×I, order 10
Flag orbits42
ConvexYes
NatureTame

The paragyrate diminished rhombicosidodecahedron (OBSA: pagydrid) is one of the 92 Johnson solids (J77). It consists of 5+5+5 triangles, 5+5+5+10 squares, 1+5+5 pentagons, and 1 decagon. It can be constructed by removing one of the pentagonal cupolaic caps of the small rhombicosidodecahedron, and rotating the opposite cap by 36°.

Vertex coordinates[edit | edit source]

A paragyrate diminished rhombicosidodecahedron of edge length 1 has vertices given by:

  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • ,
  • .

External links[edit | edit source]