Faceted rectified pentachoron

Faceted rectified pentachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Firp
Coxeter diagram	(x3/2o3o3x)/2 (/2)
Elements
Cells	5 tetrahedra, 10 triangular prisms
Faces	20 triangles, 15 squares
Edges	30
Vertices	10
Vertex figure	Triangular retroprism, edge lengths 1 (base) and √2 (sides)
Edge figure	tet 3 trip 4 trip 4 trip 3
Measures (edge length 1)
Circumradius	$\frac{\sqrt{15}}{5} ≈ 0.77460$
Hypervolume	$\frac{\sqrt5}{32} ≈ 0.069877$
Dichoral angles	Tet–3–trip: $\arccos\left(\frac{\sqrt6}{4}\right) ≈ 52.23876°$
	Trip–4–trip: $\arccos\left(\frac23\right) ≈ 48.18968°$
Central density	3
Number of external pieces	115
Level of complexity	23
Related polytopes
Army	Rap
Regiment	Rap
Conjugate	None
Convex core	Joined pentachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	No
Nature	Tame

The faceted rectified pentachoron, or firp, is a nonconvex uniform polychoron that consists of 5 regular tetrahedra and 10 triangular prisms. Two tetrahedra and six triangular prisms join at each vertex.

It is also the crossed tetrahedral cuploid.

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the rectified pentachoron.

Gallery

• 

  Cross-sections

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  Cross-section animation

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  One of each type of cell shown

• 

  One of each type of cell shown, rotating

External links

• Bowers, Jonathan. "Category 3: Triangular Rectates" (#40).

• Klitzing, Richard. "firp".