Polytope of Type {3,2,4,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,4,10}*1920
if this polytope has a name.
Group : SmallGroup(1920,205028)
Rank : 6
Schlafli Type : {3,2,4,4,10}
Number of vertices, edges, etc : 3, 3, 4, 8, 20, 10
Order of s0s1s2s3s4s5 : 60
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {3,2,2,4,10}*960, {3,2,4,2,10}*960
4-fold quotients : {3,2,4,2,5}*480, {3,2,2,2,10}*480
5-fold quotients : {3,2,4,4,2}*384
8-fold quotients : {3,2,2,2,5}*240
10-fold quotients : {3,2,2,4,2}*192, {3,2,4,2,2}*192
20-fold quotients : {3,2,2,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := (24,29)(25,30)(26,31)(27,32)(28,33)(34,39)(35,40)(36,41)(37,42)(38,43)
(64,69)(65,70)(66,71)(67,72)(68,73)(74,79)(75,80)(76,81)(77,82)(78,83);;
s3 := ( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)(13,33)
(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)(44,64)
(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)(54,74)(55,75)
(56,76)(57,77)(58,78)(59,79)(60,80)(61,81)(62,82)(63,83);;
s4 := ( 4,44)( 5,48)( 6,47)( 7,46)( 8,45)( 9,49)(10,53)(11,52)(12,51)(13,50)
(14,54)(15,58)(16,57)(17,56)(18,55)(19,59)(20,63)(21,62)(22,61)(23,60)(24,74)
(25,78)(26,77)(27,76)(28,75)(29,79)(30,83)(31,82)(32,81)(33,80)(34,64)(35,68)
(36,67)(37,66)(38,65)(39,69)(40,73)(41,72)(42,71)(43,70);;
s5 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,25)(26,28)
(29,30)(31,33)(34,35)(36,38)(39,40)(41,43)(44,45)(46,48)(49,50)(51,53)(54,55)
(56,58)(59,60)(61,63)(64,65)(66,68)(69,70)(71,73)(74,75)(76,78)(79,80)
(81,83);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(83)!(2,3);
s1 := Sym(83)!(1,2);
s2 := Sym(83)!(24,29)(25,30)(26,31)(27,32)(28,33)(34,39)(35,40)(36,41)(37,42)
(38,43)(64,69)(65,70)(66,71)(67,72)(68,73)(74,79)(75,80)(76,81)(77,82)(78,83);
s3 := Sym(83)!( 4,24)( 5,25)( 6,26)( 7,27)( 8,28)( 9,29)(10,30)(11,31)(12,32)
(13,33)(14,34)(15,35)(16,36)(17,37)(18,38)(19,39)(20,40)(21,41)(22,42)(23,43)
(44,64)(45,65)(46,66)(47,67)(48,68)(49,69)(50,70)(51,71)(52,72)(53,73)(54,74)
(55,75)(56,76)(57,77)(58,78)(59,79)(60,80)(61,81)(62,82)(63,83);
s4 := Sym(83)!( 4,44)( 5,48)( 6,47)( 7,46)( 8,45)( 9,49)(10,53)(11,52)(12,51)
(13,50)(14,54)(15,58)(16,57)(17,56)(18,55)(19,59)(20,63)(21,62)(22,61)(23,60)
(24,74)(25,78)(26,77)(27,76)(28,75)(29,79)(30,83)(31,82)(32,81)(33,80)(34,64)
(35,68)(36,67)(37,66)(38,65)(39,69)(40,73)(41,72)(42,71)(43,70);
s5 := Sym(83)!( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,25)
(26,28)(29,30)(31,33)(34,35)(36,38)(39,40)(41,43)(44,45)(46,48)(49,50)(51,53)
(54,55)(56,58)(59,60)(61,63)(64,65)(66,68)(69,70)(71,73)(74,75)(76,78)(79,80)
(81,83);
poly := sub<Sym(83)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;
to this polytope