Rank4
TypeUniform dual
Notation
Coxeter diagramo4m3o3o ()
Elements
Cells32 triangular tegums
Faces96 isosceles triangles
Edges24+64
Vertices8+16
Vertex figure16 tetrahedra, 8 rhombic dodecahedra
Measures (edge length 1)
Dichoral angle${\displaystyle \arccos \left(-{\frac {2}{3}}\right)\approx 131.81031^{\circ }}$
Central density1
Related polytopes
DualRectified tesseract
Abstract & topological properties
Flag count1152
Euler characteristic0
OrientableYes
Properties
SymmetryB4, order 384
ConvexYes
NatureTame

The joined hexadecachoron, joined square duotegum, or transitional digonal double tegmotrapezohedroid, also known as the triangular-tegmatic triacontadichoron or tibbit, is a convex isochoric polychoron with 32 triangular tegums as cells. It can be obtained as the dual of the rectified tesseract.

As the joined square duotegum, it is the square member of an infinite family of isochoric joined duotegums.

It can also be obtained as the convex hull of a tesseract and a hexadecachoron, where the edges of the hexadecachoron are ${\displaystyle {\frac {3{\sqrt {2}}}{2}}\approx 2.12132}$ times the length of those of the tesseract.

The ratio between the longest and shortest edges is 1:${\displaystyle {\frac {3{\sqrt {14}}}{7}}}$ ≈ 1:1.60357. Each face is an isosceles triangle that uses one long and two short edges.

## Variations

The joined hexadecachoron has a variant with D4 symmetry that remains isochoric. In this variant the tegums become apiculated triangular pyramids, and the variant could be called an apiculatotripyramidal triacontadichoron.

## Isogonal derivatives

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