Pentagonal antitegum

Pentagonal antitegum
Rank	3
Type	Uniform dual
Space	Spherical
Notation
Bowers style acronym	Pat
Coxeter diagram	p2p10o ()
Elements
Faces	10 kites
Edges	10+10
Vertices	2+10
Vertex figure	2 pentagons, 10 triangles
Measures (edge length 1)
Dihedral angle	$\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$
Central density	1
Related polytopes
Army	Pat
Regiment	Pat
Dual	Pentagonal antiprism
Conjugate	Pentagrammic retroantitegum
Abstract & topological properties
Euler characteristic	2
Surface	Sphere
Orientable	Yes
Genus	0
Properties
Symmetry	I2(10)×A1/2, order 20
Convex	Yes
Nature	Tame

The pentagonal antitegum or pat, also known as the pentagonal trapezohedron, is an antitegum based on the pentagon, constructed as the dual of a pentagonal antiprism. It has 10 kites as faces, with 2 order–5 and 10 order–3 vertices.

Each face of this polyhedron is a kite with its longer edges $\frac{3+\sqrt5}{4} \approx 2.61803$ times the length of its shorter edges. These kites have 3 angles measuring 108° and 1 measuring 36°.

The pentagonal antitegum can be constructed from the regular dodecahedron by augmenting tall pyramids on two opposite faces.

External links

• Klitzing, Richard. "p2p5p".

• Wikipedia Contributors. "Pentagonal trapezohedron".
• McCooey, David. "Pentagonal Trapezohedron"