Joined hexadecachoron

Joined hexadecachoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Coxeter diagram	o4m3o3o ()
Elements
Cells	32 triangular tegums
Faces	96 isosceles triangles
Edges	24+64
Vertices	8+16
Vertex figure	16 tetrahedra, 8 rhombic dodecahedra
Measures (edge length 1)
Dichoral angle	$\arccos \left(-{\frac {2}{3}}\right)\approx 131.81031^{\circ }$
Central density	1
Related polytopes
Dual	Rectified tesseract
Abstract & topological properties
Flag count	1152
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	Yes
Nature	Tame

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 ${\frac {3{\sqrt {2}}}{2}}\approx 2.12132$ times the length of those of the tesseract.

The ratio between the longest and shortest edges is 1:${\frac {3{\sqrt {14}}}{7}}$ ≈ 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:

• Triangular tegum (32): Rectified icositetrachoron
• Isosceles triangle (96): Semi-uniform small rhombated tesseract
• Edge (24): Icositetrachoron
• Edge (64): Semi-uniform small disprismatotesseractihexadecachoron
• Vertex (8): Hexadecachoron
• Vertex (16): Tesseract

External links

• Klitzing, Richard. "tibbit".