# Joined icositetrachoron

Joined icositetrachoron
Rank4
TypeUniform dual
SpaceSpherical
Notation
Bowers style acronymJico
Coxeter diagramo3m4o3o
Elements
Cells96 triangular tegums
Faces288 isosceles triangles
Edges96+144
Vertices24+24
Vertex figure24 octahedra, 24 rhombic dodecahedra
Measures (edge length 1)
Dichoral angle${\displaystyle \arccos\left(-\frac56\right) ≈ 146.44269°}$
Central density1
Related polytopes
ArmyJico
RegimentJico
DualRectified icositetrachoron
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryF4, order 1152
ConvexYes
NatureTame

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 ${\displaystyle \frac{3\sqrt2}{4} ≈ 1.06066}$ times that of the other.

The ratio between the longest and shortest edges is 1:${\displaystyle \frac{3\sqrt5}{5}}$ ≈ 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 BC4 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: