Joined hexacosichoron

Joined hexacosichoron
(OFF file)
Rank	4
Type	Uniform dual
Space	Spherical
Notation
Bowers style acronym	Tibbic
Coxeter diagram	o5m3o3o ()
Elements
Cells	1200 triangular tegums
Faces	3600 isosceles triangles
Edges	720+2400
Vertices	120+600
Vertex figure	600 tetrahedra, 120 rhombic triacontahedra
Measures (edge length 1)
Dichoral angle	$\arccos\left(-\frac{5+3\sqrt5}{12}\right) \approx 167.33892^\circ$
Central density	1
Related polytopes
Dual	Rectified hecatonicosachoron
Abstract & topological properties
Flag count	43200
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	Yes
Nature	Tame

Not to be confused with Joined hecatonicosachoron.

The joined hexacosichoron, also known as the triangular-tegmatic chiliadiacosichoron or tibbic, is a convex isochoric polychoron with 1200 triangular tegums as cells. It can be obtained as the dual of the rectified hecatonicosachoron.

It can also be obtained as the convex hull of a hecatonicosachoron and a hexacosichoron, where the edges of the hexacosichoron are $\frac{3(1+\sqrt5)}{4} \approx 2.42705$ times the length of those of the hecatonicosachoron.

The ratio between the longest and shortest edges is 1:$3\sqrt{\frac{9+\sqrt5}{38}}$ ≈ 1:1.63131. Each face is an isosceles triangle that uses one long and two short edges.

Isogonal derivatives

Substitution by vertices of these following elements will produce these convex isogonal polychora:

• Triangular tegum (1200): Rectified hecatonicosachoron
• Isosceles triangle (3600): Semi-uniform small rhombated hecatonicosachoron
• Edge (720): Rectified hexacosichoron
• Edge (2400): Semi-uniform small disprismatohexacosihecatonicosachoron
• Vertex (120): Hexacosichoron
• Vertex (600): Hecatonicosachoron

External links

• Klitzing, Richard. "tibbic".