# Joined icositetrachoron

Joined icositetrachoron
Rank4
TypeUniform dual
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${\displaystyle \arccos \left(-{\frac {5}{6}}\right)\approx 146.44269^{\circ }}$
Central density1
Related polytopes
ArmyJico
RegimentJico
DualRectified icositetrachoron
Abstract & topological properties
Flag count3456
Euler characteristic0
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 ${\displaystyle {\frac {3{\sqrt {2}}}{4}}\approx 1.06066}$ times that of the other.

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