Joined pentachoron

Joined pentachoron
(OFF file)
Rank	4
Type	Uniform dual
Notation
Bowers style acronym	Jop
Coxeter diagram	o3m3o3o ()
Elements
Cells	10 triangular tegums
Faces	30 isosceles triangles
Edges	10+20
Vertices	5+5
Vertex figure	5 tetrahedra, 5 cubes
Measures (short edge length 1)
Dichoral angle	$\arccos \left(-{\frac {1}{6}}\right)\approx 99.59407^{\circ }$
Central density	1
Related polytopes
Army	Jop
Regiment	Jop
Dual	Rectified pentachoron
Abstract & topological properties
Flag count	360
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4, order 120
Convex	Yes
Nature	Tame

The joined pentachoron or jop, also known as the triangular-tegmatic decachoron or tibbid, is a convex isochoric polychoron with 10 triangular tegums as cells. It can be obtained as the dual of the rectified pentachoron.

It can also be obtained as the convex hull of 2 dually-oriented pentachora, where one has edge length ${\frac {3}{2}}=1.5$ times that of the other.

The ratio between the longest and shortest edges is 1:1.5. Each face is an isosceles triangle that uses one long and two short edges.

Isogonal derivatives

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

• Triangular tegum (30): Rectified pentachoron
• Isosceles triangle (30): Semi-uniform small rhombated pentachoron
• Edge (10): Rectified pentachoron
• Edge (20): Semi-uniform small prismatodecachoron
• Vertex (5): Pentachoron
• Vertex (5): Pentachoron

External links

• Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".

• Klitzing, Richard. "tibbid".
• Quickfur. "The Joined Pentachoron".