Noble faceting of rectified pentachoron

Noble faceting of rectified pentachoron
Rank	4
Type	Noble
Space	Spherical
Elements
Cells	10 triangular toroprisms
Faces	30 isosceles triangles 15 squares
Edges	30 3-fold 15 4-fold
Vertices	10
Vertex figure	Dual of triangular toroprism
Measures (based on rectified pentachoron with edge length 1)
Edge lengths	30× $1$
	15× $\sqrt{2} \approx 1.414213562$
Circumradius	$\frac{\sqrt{15}}{5} \approx 0.7745966692$
Volume	$\frac{\sqrt{5}}{16} \approx 0.1397542486$
Related polytopes
Army	Rap
Dual	Self-dual
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	No
Nature	Wild

This self-dual noble polychoron is the vertex figure of the hexadecateron. The edges are then verfs of triangles and squares, the triangles verfs of triangular prisms, the squares verfs of octahedra, and the cells verfs of prismatointercepted pentachora.

External links

• Klitzing, Richard. "hit-verf".