Polytope of Type {2,12,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,10}*480
if this polytope has a name.
Group : SmallGroup(480,1087)
Rank : 4
Schlafli Type : {2,12,10}
Number of vertices, edges, etc : 2, 12, 60, 10
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,12,10,2} of size 960
   {2,12,10,4} of size 1920
Vertex Figure Of :
   {2,2,12,10} of size 960
   {3,2,12,10} of size 1440
   {4,2,12,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,10}*240
   3-fold quotients : {2,4,10}*160
   5-fold quotients : {2,12,2}*96
   6-fold quotients : {2,2,10}*80
   10-fold quotients : {2,6,2}*48
   12-fold quotients : {2,2,5}*40
   15-fold quotients : {2,4,2}*32
   20-fold quotients : {2,3,2}*24
   30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,10}*960a, {2,24,10}*960, {2,12,20}*960
   3-fold covers : {2,36,10}*1440, {6,12,10}*1440a, {6,12,10}*1440b, {2,12,30}*1440a, {2,12,30}*1440b
   4-fold covers : {4,12,20}*1920a, {8,12,10}*1920a, {4,24,10}*1920a, {2,12,40}*1920a, {2,24,20}*1920a, {8,12,10}*1920b, {4,24,10}*1920b, {2,12,40}*1920b, {2,24,20}*1920b, {4,12,10}*1920a, {2,12,20}*1920a, {2,48,10}*1920, {4,12,10}*1920b, {2,12,20}*1920b
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 8,13)( 9,14)(10,15)(11,16)(12,17)(23,28)(24,29)(25,30)(26,31)(27,32)
(33,48)(34,49)(35,50)(36,51)(37,52)(38,58)(39,59)(40,60)(41,61)(42,62)(43,53)
(44,54)(45,55)(46,56)(47,57);;
s2 := ( 3,38)( 4,42)( 5,41)( 6,40)( 7,39)( 8,33)( 9,37)(10,36)(11,35)(12,34)
(13,43)(14,47)(15,46)(16,45)(17,44)(18,53)(19,57)(20,56)(21,55)(22,54)(23,48)
(24,52)(25,51)(26,50)(27,49)(28,58)(29,62)(30,61)(31,60)(32,59);;
s3 := ( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)(25,27)
(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)(53,54)
(55,57)(58,59)(60,62);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(62)!(1,2);
s1 := Sym(62)!( 8,13)( 9,14)(10,15)(11,16)(12,17)(23,28)(24,29)(25,30)(26,31)
(27,32)(33,48)(34,49)(35,50)(36,51)(37,52)(38,58)(39,59)(40,60)(41,61)(42,62)
(43,53)(44,54)(45,55)(46,56)(47,57);
s2 := Sym(62)!( 3,38)( 4,42)( 5,41)( 6,40)( 7,39)( 8,33)( 9,37)(10,36)(11,35)
(12,34)(13,43)(14,47)(15,46)(16,45)(17,44)(18,53)(19,57)(20,56)(21,55)(22,54)
(23,48)(24,52)(25,51)(26,50)(27,49)(28,58)(29,62)(30,61)(31,60)(32,59);
s3 := Sym(62)!( 3, 4)( 5, 7)( 8, 9)(10,12)(13,14)(15,17)(18,19)(20,22)(23,24)
(25,27)(28,29)(30,32)(33,34)(35,37)(38,39)(40,42)(43,44)(45,47)(48,49)(50,52)
(53,54)(55,57)(58,59)(60,62);
poly := sub<Sym(62)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope