Polytope of Type {3,2,10,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,10,4,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,205028)
Rank : 6
Schlafli Type : {3,2,10,4,4}
Number of vertices, edges, etc : 3, 3, 10, 20, 8, 4
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 : {3,2,10,2,4}*960, {3,2,10,4,2}*960
4-fold quotients : {3,2,5,2,4}*480, {3,2,10,2,2}*480
5-fold quotients : {3,2,2,4,4}*384
8-fold quotients : {3,2,5,2,2}*240
10-fold quotients : {3,2,2,2,4}*192, {3,2,2,4,2}*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 := ( 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)(45,48)(46,47)(50,53)(51,52)(55,58)
(56,57)(60,63)(61,62)(65,68)(66,67)(70,73)(71,72)(75,78)(76,77)(80,83)
(81,82);;
s3 := ( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,30)(25,29)
(26,33)(27,32)(28,31)(34,40)(35,39)(36,43)(37,42)(38,41)(44,45)(46,48)(49,50)
(51,53)(54,55)(56,58)(59,60)(61,63)(64,70)(65,69)(66,73)(67,72)(68,71)(74,80)
(75,79)(76,83)(77,82)(78,81);;
s4 := ( 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);;
s5 := ( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)(13,53)
(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)(24,74)
(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,64)(35,65)
(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)(42,72)(43,73);;
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*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,
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)(45,48)(46,47)(50,53)(51,52)
(55,58)(56,57)(60,63)(61,62)(65,68)(66,67)(70,73)(71,72)(75,78)(76,77)(80,83)
(81,82);
s3 := Sym(83)!( 4, 5)( 6, 8)( 9,10)(11,13)(14,15)(16,18)(19,20)(21,23)(24,30)
(25,29)(26,33)(27,32)(28,31)(34,40)(35,39)(36,43)(37,42)(38,41)(44,45)(46,48)
(49,50)(51,53)(54,55)(56,58)(59,60)(61,63)(64,70)(65,69)(66,73)(67,72)(68,71)
(74,80)(75,79)(76,83)(77,82)(78,81);
s4 := 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);
s5 := Sym(83)!( 4,44)( 5,45)( 6,46)( 7,47)( 8,48)( 9,49)(10,50)(11,51)(12,52)
(13,53)(14,54)(15,55)(16,56)(17,57)(18,58)(19,59)(20,60)(21,61)(22,62)(23,63)
(24,74)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,64)
(35,65)(36,66)(37,67)(38,68)(39,69)(40,70)(41,71)(42,72)(43,73);
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*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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope