Gyroelongated pentagonal rotunda

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Gyroelongated pentagonal rotunda
Rank3
TypeCRF
Notation
Bowers style acronymGyepro
Elements
Faces5+5+5+5+10 triangles, 1+5 pentagons, 1 decagon
Edges5+5+5+10+10+10+10+10
Vertices5+5+5+5+10
Vertex figures10 rectangles, edge lengths 1 and (1+5)/2
 10 irregular pentagons, edge lengths 1, 1, 1, 1, (1+5)/2
 10 Isosceles trapezoids, edge lengths 1, 1, 1, (5+5)/2
Measures (edge length 1)
Volume
Dihedral angles3–3 join:
 3–3 antiprismatic:
 3–5 join:
 3–5 rotundaic:
 3–10:
Central density1
Number of external pieces37
Level of complexity26
Related polytopes
ArmyGyepro
RegimentGyepro
DualPentapentarhombidecapentagonal hemitrapezohedron
ConjugateGyroelongated pentagrammic rotunda
Abstract & topological properties
Flag count260
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH2×I, order 10
ConvexYes
NatureTame

The gyroelongated pentagonal rotunda is one of the 92 Johnson solids (J25). It consists of 5+5+5+5+10 triangles, 1+5 pentagons, and 1 decagon. It can be constructed by attaching a decagonal antiprism to the decagonal base of the pentagonal rotunda.

If a second rotunda is attached to the other decagonal base of the antiprism, the result is the gyroelongated pentagonal birotunda.

Vertex coordinates[edit | edit source]

A gyroelongated pentagonal rotunda of edge length 1 has the following vertices:

where H = is the distance between the decagonal antiprism's center and the center of one of its bases.

External links[edit | edit source]