Polytope of Type {3,2,20,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,20,8}*1920a
if this polytope has a name.
Group : SmallGroup(1920,148893)
Rank : 5
Schlafli Type : {3,2,20,8}
Number of vertices, edges, etc : 3, 3, 20, 80, 8
Order of s0s1s2s3s4 : 120
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,20,4}*960, {3,2,10,8}*960
4-fold quotients : {3,2,20,2}*480, {3,2,10,4}*480
5-fold quotients : {3,2,4,8}*384a
8-fold quotients : {3,2,10,2}*240
10-fold quotients : {3,2,4,4}*192, {3,2,2,8}*192
16-fold quotients : {3,2,5,2}*120
20-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
40-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 5, 8)( 6, 7)(10,13)(11,12)(15,18)(16,17)(20,23)(21,22)(25,28)(26,27)
(30,33)(31,32)(35,38)(36,37)(40,43)(41,42)(44,64)(45,68)(46,67)(47,66)(48,65)
(49,69)(50,73)(51,72)(52,71)(53,70)(54,74)(55,78)(56,77)(57,76)(58,75)(59,79)
(60,83)(61,82)(62,81)(63,80);;
s3 := ( 4,45)( 5,44)( 6,48)( 7,47)( 8,46)( 9,50)(10,49)(11,53)(12,52)(13,51)
(14,60)(15,59)(16,63)(17,62)(18,61)(19,55)(20,54)(21,58)(22,57)(23,56)(24,65)
(25,64)(26,68)(27,67)(28,66)(29,70)(30,69)(31,73)(32,72)(33,71)(34,80)(35,79)
(36,83)(37,82)(38,81)(39,75)(40,74)(41,78)(42,77)(43,76);;
s4 := (14,19)(15,20)(16,21)(17,22)(18,23)(34,39)(35,40)(36,41)(37,42)(38,43)
(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)(64,74)
(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(83)!(2,3);
s1 := Sym(83)!(1,2);
s2 := Sym(83)!( 5, 8)( 6, 7)(10,13)(11,12)(15,18)(16,17)(20,23)(21,22)(25,28)
(26,27)(30,33)(31,32)(35,38)(36,37)(40,43)(41,42)(44,64)(45,68)(46,67)(47,66)
(48,65)(49,69)(50,73)(51,72)(52,71)(53,70)(54,74)(55,78)(56,77)(57,76)(58,75)
(59,79)(60,83)(61,82)(62,81)(63,80);
s3 := Sym(83)!( 4,45)( 5,44)( 6,48)( 7,47)( 8,46)( 9,50)(10,49)(11,53)(12,52)
(13,51)(14,60)(15,59)(16,63)(17,62)(18,61)(19,55)(20,54)(21,58)(22,57)(23,56)
(24,65)(25,64)(26,68)(27,67)(28,66)(29,70)(30,69)(31,73)(32,72)(33,71)(34,80)
(35,79)(36,83)(37,82)(38,81)(39,75)(40,74)(41,78)(42,77)(43,76);
s4 := Sym(83)!(14,19)(15,20)(16,21)(17,22)(18,23)(34,39)(35,40)(36,41)(37,42)
(38,43)(44,54)(45,55)(46,56)(47,57)(48,58)(49,59)(50,60)(51,61)(52,62)(53,63)
(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(73,83);
poly := sub<Sym(83)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope