Polytope of Type {2,10,12}

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

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