Acronym | sody | ||||||
Name |
small deckishecatonicosachoron, snub decahecatonicosachoron, compound of 10 ex in hi army, compound of 2 spohi | ||||||
Coxeter symbol | 2{5,3,3}[10{3,3,5}] | ||||||
Circumradius | (1+sqrt(5))/2 = 1.618034 | ||||||
Vertex figure |
© | ||||||
General of army | hi | ||||||
Embedding |
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Confer | |||||||
External links |
This compound occurs in different forms depending on whether the vertices (coincident by 2) will be counted separately (type A), or will be identified (type C), or whether incident vertices, coplanar triangles, and corealmic tets will be united each (type E). All these would use 10 hexacosachora for compound components. – Two of those cases could be considered on base of the 5 hexacosachora compound (spohi) instead, i.e. using just 2 such components. That then gives rise to (type B) with no identifications, (type D) with identification of vertices only. – As (type E) already cross-connects the tets of either spohi, therefore there will be no according type using those for bases here.
Case E is interesting in that it points out that the altogether 6000 tets here form 2 different corealmic cell clusters. One of those is the well-known compound of 10 tets within an encasing doe, i.e. "e". In fact, each of the 120 does of the encasing hi of sody itself gives rise to that cell compound. But even the remainder of 4800 tet forms non-uniform axial compounds in the sense of mutually rotated pairs of trigonal pyramids with a single common tip each. The corresponding base, a polygonal compound of 2 triangles, with x3f as encasing hull, then connects those 2 cell clusters.
(Type A) - no identifications 1200 ♦ 12 | 30 | 20 || 1 verf: ike -----+------+-------+------++--- 2 | 7200 | 5 | 5 || 1 -----+------+-------+------++--- 3 | 3 | 12000 | 2 || 1 -----+------+-------+------++--- 4 | 6 | 4 | 6000 || 1 tet -----+------+-------+------++--- 120 | 720 | 1200 | 600 || 10 ex
(Type B) - no identifications, but as 2 spohi comp. 1200 ♦ 12 | 30 | 20 || 1 verf: ike -----+------+-------+------++-- 2 | 7200 | 5 | 5 || 1 -----+------+-------+------++-- 3 | 3 | 12000 | 2 || 1 -----+------+-------+------++-- 4 | 6 | 4 | 6000 || 1 tet -----+------+-------+------++-- 600 | 3600 | 6000 | 3000 || 2 spohi
(Type C) - identifying incident vertices only 600 ♦ 24 | 60 | 40 || 2 verf: siddo ----+------+-------+------++--- 2 | 7200 | 5 | 5 || 1 ----+------+-------+------++--- 3 | 3 | 12000 | 2 || 1 ----+------+-------+------++--- 4 | 6 | 4 | 6000 || 1 tet ----+------+-------+------++--- 120 | 720 | 1200 | 600 || 10 ex
(Type D) - identifying incident vertices only, but as 2 spohi comp. 600 ♦ 24 | 60 | 40 || 2 verf: siddo ----+------+-------+------++-- 2 | 7200 | 5 | 5 || 1 ----+------+-------+------++-- 3 | 3 | 12000 | 2 || 1 ----+------+-------+------++-- 4 | 6 | 4 | 6000 || 1 tet ----+------+-------+------++-- 600 | 3600 | 6000 | 3000 || 2 spohi
(Type E) - identifying vertices, coplanar triangles, and corealmic tets 600 ♦ 24 | 24 36 | 4 28 || 2 verf: siddo ----+------+-----------+----------++--- 2 | 7200 | 2 3 | 1 4 || 1 ----+------+-----------+----------++--- 6 | 6 | 2400 * | 1 1 || 2 red+blue 3 | 3 | * 7200 | 0 2 || 1 yellow+green/orange+magenta ----+------+-----------+----------++--- 20 | 60 | 20 0 | 120 * || 10 red+blue e (10-tet comp.) 7 | 12 | 1 6 | * 2400 || 2 yellow/orange + green/magenta 2-trig.pyr comp. ----+------+-----------+----------++--- 120 | 720 | 960 240 | 120 480 || 10 red+yellow/blue+green ex
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