Elongated pentagonal rotunda

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Elongated pentagonal rotunda
Rank3
TypeCRF
Notation
Bowers style acronymEpro
Coxeter diagramofxx5xoxx&#xt
Elements
Faces
Edges5+5+5+5+5+10+10+10
Vertices5+5+10+10
Vertex figures5 rectangles, edge lengths 1 and (1+5)/2
 10 irregular tetragons, edge lengths 1, (1+5)/2, 2, 2
 10 isosceles triangles, edge lengths (5+5)/2, 2, 2
Measures (edge length 1)
Volume
Dihedral angles3–4:
 5–4:
 4–4: 144°
 3–5:
 4–10: 90°
Central density1
Number of external pieces27
Level of complexity22
Related polytopes
ArmyEpro
RegimentEpro
DualDecakis order-10 truncated semibisected pentagonal rhombitrapezohedron
ConjugateElongated pentagrammic rotunda
Abstract & topological properties
Flag count220
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH2×I, order 10
Flag orbits22
ConvexYes
NatureTame

The elongated pentagonal rotunda (OBSA: epro) is one of the 92 Johnson solids (J21). It consists of 5+5 triangles, 5+5 squares, 1+5 pentagons, and 1 decagon. It can be constructed by attaching a decagonal prism to the decagonal base of the pentagonal rotunda.

If a second rotunda is attached to the other decagonal base of the prism in the same orientation, the result is the elongated pentagonal orthobirotunda. If the second rotunda is rotated 36° instead, the result is the elongated pentagonal gyrobirotunda.

Vertex coordinates[edit | edit source]

An elongated pentagonal rotunda of edge length 1 has the following vertices:

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

Related polyhedra[edit | edit source]

The three tunnellings of the elongated pentagonal rotunda. The convex hull is shown as a transparency.

Three quasi-convex Stewart toroids are made by tunnelling the elongated pentagonal rotunda. Two of these are distinct elongations of the tunnelled pentagonal rotunda.

External links[edit | edit source]