Notched triacontachoron

Notched triacontachoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	m3o3m3o ()
Elements
Cells	30 notches
Faces	30 isosceles triangles, 60 scalene triangles
Edges	10+20+20+30
Vertices	5+5+10
Vertex figure	10 triangular bipyramids, 5 cubes, 5 rhombic dodecahedra
Measures (edge length 1)
Dichoral angle	$\arccos \left(-{\frac {9}{14}}\right)\approx 130.0052^{\circ }$
Central density	1
Related polytopes
Dual	Small rhombated pentachoron
Abstract & topological properties
Flag count	1080
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	Yes
Nature	Tame

The notched triacontachoron is a convex isochoric polychoron with 30 notches as cells. It can be obtained as the dual of the small rhombated pentachoron.

It can also be constructed as the convex hull of 2 dual pentachora and a rectified pentachoron. If the smaller pentachoron has edge length 1, the larger pentachoron has edge length ${\frac {3}{2}}=1.5$ and the rectified pentachoron has edge length ${\frac {6}{7}}\approx 0.85714$.

The ratio between the longest and shortest edges is 1:${\frac {21}{8}}$ = 1:2.625.

External links

• Klitzing, Richard. "dusrip".