Joined icositetrachoron

Joined icositetrachoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Bowers style acronym	Jico
Coxeter diagram	o3m4o3o ()
Elements
Cells	96 triangular tegums
Faces	288 isosceles triangles
Edges	96+144
Vertices	24+24
Vertex figure	24 octahedra, 24 rhombic dodecahedra
Measures (edge length 1)
Dichoral angle	$\arccos \left(-{\frac {5}{6}}\right)\approx 146.44269^{\circ }$
Central density	1
Related polytopes
Army	Jico
Regiment	Jico
Dual	Rectified icositetrachoron
Abstract & topological properties
Flag count	3456
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4, order 1152
Convex	Yes
Nature	Tame

The joined icositetrachoron or jico, also known as the triangular-tegmatic enneacontahexachoron or tabene, is a convex isochoric polychoron with 96 triangular tegums as cells. It can be obtained as the dual of the rectified icositetrachoron.

It can also be obtained as the convex hull of 2 dually-oriented icositetrachora, where one has edge length ${\frac {3{\sqrt {2}}}{4}}\approx 1.06066$ times that of the other.

The ratio between the longest and shortest edges is 1:${\frac {3{\sqrt {5}}}{5}}$ ≈ 1:1.34164. Each face is an isosceles triangle that uses one long and two short edges.

Variations

The joined icositetrachoron has variants that remain isochoric under B₄ symmetry (called the great notched enneacontahexachoron) and D₄ symmetry (called the skewed notched enneacontahexachoron).

Isogonal derivatives

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

• Triangular tegum (96): Rectified icositetrachoron
• Isosceles triangle (288): Small rhombated icositetrachoron
• Edge (96): Rectified icositetrachoron
• Edge (144): Semi-uniform small prismatotetracontoctachoron
• Vertex (24): Icositetrachoron
• Vertex (24): Icositetrachoron

External links

• Klitzing, Richard. "jico".