Gyroelongated pentagonal cupola

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Gyroelongated pentagonal cupola
Rank3
TypeCRF
Notation
Bowers style acronymGyepcu
Coxeter diagramoxo10sox&#xt
Elements
Faces5+5+5+10 triangles, 5 squares, 1 pentagon, 1 decagon
Edges5+5+5+10+10+10+10
Vertices5+5+5+10
Vertex figures5 isosceles trapezoids, edge lengths 1, 2, (1+5)/2, 2
 10 irregular pentagons, edge lengths 1, 1, 1, 1, 2
 10 isosceles trapezoids, edge lengths 1, 1, 1, (5+5)/2
Measures (edge length 1)
Volume
Dihedral angles3–3 antiprismatic:
 3–4 cupolaic:
 4–5:
 3–3 join:
 3–4 join:
 3–10:
Central density1
Number of external pieces32
Level of complexity22
Related polytopes
ArmyGyepcu
RegimentGyepcu
DualPentadeltadecapentagonal hemitrapezohedron
ConjugateGyroelongated retrograde pentagrammic cupola
Abstract & topological properties
Flag count220
Euler characteristic2
SurfaceSphere
OrientableYes
Genus0
Properties
SymmetryH2×I, order 10
ConvexYes
NatureTame

The gyroelongated pentagonal cupola is one of the 92 Johnson solids (J24). It consists of 5+5+5+10 triangles, 5 squares, 1 pentagon, and 1 decagon. It can be constructed by attaching a decagonal antiprism to the decagonal base of the pentagonal cupola.

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

Vertex coordinates[edit | edit source]

A gyroelongated pentagonal cupola 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]