Small blendic disprismatodishecatonicosachoron

Small blendic disprismatodishecatonicosachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Sabbadipady
Coxeter diagram	x5/3x5o3o5/2xØ*a
Elements
Cells	720 pentagonal prisms, 720 pentagrammic prisms, 120 great stellated dodecahedra, 120 quasitruncated small stellated dodecahedra
Faces	3600 squares, 1440 pentagons, 1440 pentagrams, 720 decagrams
Edges	1200+3600+3600
Vertices	2400
Vertex figure	Augmented triangular antipodium, edge lengths (√5–1)/2 (unaugmented base), (1+√5)/2 (augmented base), √2 (antipodium sides), and √(5–√5)/2 (augment sides)
Measures (edge length 1)
Circumradius	2
Hypervolume	$3\left(190+39\sqrt5\right) ≈ 831.61995$
Dichoral angles	Gissid–5/2–stip: 162°
	Stip–4–pip: $\arccos\left(-\frac{2\sqrt5}{5}\right) ≈ 153.43495^\circ$
	Quit sissid–10/3–quit sissid: 144°
	Quit sissid–5–pip: 126°
Number of external pieces	18840
Level of complexity	65
Related polytopes
Army	Sidpixhi
Regiment	Sabbadipady
Conjugate	Great blendic disprismatodishecatonicosachoron
Convex core	Chamfered hecatonicosachoron
Abstract & topological properties
Euler characteristic	–480
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The small blendic disprismatodishecatonicosachoron, or sabbadipady, is a nonconvex uniform polychoron that consists of 120 great stellated dodecahedra, 120 quasitruncated small stellated dodecahedra, 720 pentagonal prisms, and 720 pentagrammic prisms. 1 great stellated dodecahedron, 3 pentagonal prisms, 3 pentagrammic prisms, and 3 quasitruncated small stellated dodecahedra join at each vertex.

It contains the vertices and edges of a truncated great grand hecatonicosachoron, quasitruncated small stellated hecatonicosachoron, and small disprismatodishecatonicosachoron, which each use all of its vertices. It can also be constructed as the blend of the latter two, with the common dodecahedral cells blending out.

Cross-sections

Vertex coordinates

The vertices of a small blendic disprismatodishecatonicosachoron of edge length 1 are all permutations of:

• $\left(±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{5+\sqrt5}{4}\right),$
• $\left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+3\sqrt5}{4}\right),$
• $\left(±\frac{\sqrt5-1}{4},\,±\frac{5-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{3+\sqrt5}{4}\right),$
• $\left(±\frac12,\,±\frac12,\,±\frac{\sqrt5}{2},\,±\frac32\right),$
• $\left(±\frac12,\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$
• $\left(±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{4}\,±\frac{1+\sqrt5}{4},\,±\frac{3\sqrt5-1}{4}\right),$

along with the even permutations of:

• $\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac32\right),$
• $\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{1+3\sqrt5}{4},\,±\frac12\right),$
• $\left(0,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{2},\,±1\right),$
• $\left(0,\,±\frac12,\,±\frac{3\sqrt5-1}{2},\,±\frac{3+\sqrt5}{4}\right),$
• $\left(0,\,±\frac12,\,±\frac{5+\sqrt5}{4},\,±\frac{5-\sqrt5}{4}\right),$
• $\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac{1+\sqrt5}{2},\,±\frac{\sqrt5}{2}\right),$
• $\left(±\frac{3-\sqrt5}{4},\,±1,\,±\frac{\sqrt5}{2},\,±\frac{3+\sqrt5}{4}\right),$
• $\left(±\frac{\sqrt5-1}{4},\,±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{5+\sqrt5}{4}\right),$
• $\left(±\frac{\sqrt5-1}{4},\,±1,\,±\frac32,\,±\frac{1+\sqrt5}{4}\right),$
• $\left(±\frac12,\,±\frac{5-\sqrt5}{4},\,±\frac{1+\sqrt5}{4},\,±\frac{1+\sqrt5}{2}\right),$
• $\left(±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4},\,±\frac{3+\sqrt5}{4},\,±\frac{\sqrt5}{2}\right).$

Related polychora

The small blendic disprismatodishecatonicosachoron is the colonel of a regiment that includes 12 uniform members, along with 4 fissaries and 3 mixed compounds.

External links

• Bowers, Jonathan. "Category 26: Blends" (#1462).

• Klitzing, Richard. "sabbadipady".