Polytope of Type {10,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12}*240
Also Known As : {10,12|2}. if this polytope has another name.
Group : SmallGroup(240,136)
Rank : 3
Schlafli Type : {10,12}
Number of vertices, edges, etc : 10, 60, 12
Order of s₀s₁s₂ : 60
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,12,2} of size 480
   {10,12,4} of size 960
   {10,12,4} of size 960
   {10,12,4} of size 960
   {10,12,3} of size 960
   {10,12,6} of size 1440
   {10,12,6} of size 1440
   {10,12,6} of size 1440
   {10,12,3} of size 1440
   {10,12,8} of size 1920
   {10,12,8} of size 1920
   {10,12,4} of size 1920
   {10,12,4} of size 1920
   {10,12,4} of size 1920
   {10,12,6} of size 1920
   {10,12,6} of size 1920
Vertex Figure Of :
   {2,10,12} of size 480
   {4,10,12} of size 960
   {5,10,12} of size 1200
   {3,10,12} of size 1440
   {5,10,12} of size 1440
   {6,10,12} of size 1440
   {8,10,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,6}*120
   3-fold quotients : {10,4}*80
   5-fold quotients : {2,12}*48
   6-fold quotients : {10,2}*40
   10-fold quotients : {2,6}*24
   12-fold quotients : {5,2}*20
   15-fold quotients : {2,4}*16
   20-fold quotients : {2,3}*12
   30-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,24}*480, {20,12}*480
   3-fold covers : {10,36}*720, {30,12}*720a, {30,12}*720b
   4-fold covers : {10,48}*960, {20,12}*960a, {20,24}*960a, {40,12}*960a, {20,24}*960b, {40,12}*960b, {20,12}*960b
   5-fold covers : {50,12}*1200, {10,60}*1200a, {10,60}*1200b
   6-fold covers : {10,72}*1440, {20,36}*1440, {30,24}*1440a, {60,12}*1440a, {30,24}*1440b, {60,12}*1440b
   7-fold covers : {10,84}*1680, {70,12}*1680
   8-fold covers : {40,12}*1920a, {20,24}*1920a, {40,24}*1920a, {40,24}*1920b, {40,24}*1920c, {40,24}*1920d, {80,12}*1920a, {20,48}*1920a, {80,12}*1920b, {20,48}*1920b, {40,12}*1920b, {20,24}*1920b, {20,12}*1920a, {10,96}*1920, {40,12}*1920e, {40,12}*1920f, {20,24}*1920c, {20,24}*1920d, {20,12}*1920c
Permutation Representation (GAP) :

s0 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)
(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44)(47,50)(48,49)(52,55)
(53,54)(57,60)(58,59);;
s1 := ( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,17)(18,20)(21,27)
(22,26)(23,30)(24,29)(25,28)(31,47)(32,46)(33,50)(34,49)(35,48)(36,57)(37,56)
(38,60)(39,59)(40,58)(41,52)(42,51)(43,55)(44,54)(45,53);;
s2 := ( 1,36)( 2,37)( 3,38)( 4,39)( 5,40)( 6,31)( 7,32)( 8,33)( 9,34)(10,35)
(11,41)(12,42)(13,43)(14,44)(15,45)(16,51)(17,52)(18,53)(19,54)(20,55)(21,46)
(22,47)(23,48)(24,49)(25,50)(26,56)(27,57)(28,58)(29,59)(30,60);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(60)!( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)
(23,24)(27,30)(28,29)(32,35)(33,34)(37,40)(38,39)(42,45)(43,44)(47,50)(48,49)
(52,55)(53,54)(57,60)(58,59);
s1 := Sym(60)!( 1, 2)( 3, 5)( 6,12)( 7,11)( 8,15)( 9,14)(10,13)(16,17)(18,20)
(21,27)(22,26)(23,30)(24,29)(25,28)(31,47)(32,46)(33,50)(34,49)(35,48)(36,57)
(37,56)(38,60)(39,59)(40,58)(41,52)(42,51)(43,55)(44,54)(45,53);
s2 := Sym(60)!( 1,36)( 2,37)( 3,38)( 4,39)( 5,40)( 6,31)( 7,32)( 8,33)( 9,34)
(10,35)(11,41)(12,42)(13,43)(14,44)(15,45)(16,51)(17,52)(18,53)(19,54)(20,55)
(21,46)(22,47)(23,48)(24,49)(25,50)(26,56)(27,57)(28,58)(29,59)(30,60);
poly := sub<Sym(60)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope