Pentagonal-pentagrammic duotegum

Pentagonal-pentagrammic duotegum
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Bowers style acronym	Stapedit
Coxeter diagram	m5o2m5/2o
Elements
Cells	25 tetrahedra
Faces	25+25 triangles
Edges	5+5+25
Vertices	5+5
Vertex figure	5 pentagonal tegums, 5 pentagrammic tegums
Measures (edge length 1)
Inradius	$\frac{\sqrt2}{2} ≈ 0.70711$
Hypervolume	$\frac{25}{48} ≈ 0.52083$
Related polytopes
Army	Stapedit
Regiment	Stapedit
Dual	Pentagonal-pentagrammic duoprism
Conjugate	Pentagonal-pentagrammic duotegum
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H2×H2, order 100
Convex	No
Nature	Tame

The pentagonal-pentagrammic duotegum, also known as the 5-5/2 duotegum, is a duotegum that consists of 25 regular tetrahedra and 10 vertices.

This is one of only two 4D duotegums that can be made to have regular tetrahedral cells and equilateral triangular faces. The other is the square duotegum, which is the regular hexadecachoron.

Vertex coordinates

The vertices of a pentagonal-pentagrammic duotegum of edge length 1 are given by:

• $\left(±\frac{1}{2},\, -\sqrt{\frac{5+2\sqrt{5}}{20}},\,0,\,0\right),$
• $\left(±\frac{1+\sqrt{5}}{4},\, \sqrt{\frac{5-\sqrt{5}}{40}},\,0,\,0\right),$
• $\left(0,\, \sqrt{\frac{5+\sqrt{5}}{10}},\,0,\,0\right),$
• $\left(0,\,0,\,±\frac12,\,-\sqrt{\frac{5-2\sqrt5}{20}}\right),$
• $\left(0,\,0,\,±\frac{\sqrt5-1}{4},\,\sqrt{\frac{5+\sqrt5}{40}}\right),$
• $\left(0,\,0,\,0,\,-\sqrt{\frac{5-\sqrt5}{10}}\right).$

External links

• Klitzing, Richard. "stapedit".