Polytope of Type {4,2,10,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,10,12}*1920
if this polytope has a name.
Group : SmallGroup(1920,208125)
Rank : 5
Schlafli Type : {4,2,10,12}
Number of vertices, edges, etc : 4, 4, 10, 60, 12
Order of s₀s₁s₂s₃s₄ : 60
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,2,10,12}*960, {4,2,10,6}*960
   3-fold quotients : {4,2,10,4}*640
   4-fold quotients : {2,2,10,6}*480
   5-fold quotients : {4,2,2,12}*384
   6-fold quotients : {2,2,10,4}*320, {4,2,10,2}*320
   10-fold quotients : {2,2,2,12}*192, {4,2,2,6}*192
   12-fold quotients : {4,2,5,2}*160, {2,2,10,2}*160
   15-fold quotients : {4,2,2,4}*128
   20-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96
   24-fold quotients : {2,2,5,2}*80
   30-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   40-fold quotients : {2,2,2,3}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)(27,28)
(31,34)(32,33)(36,39)(37,38)(41,44)(42,43)(46,49)(47,48)(51,54)(52,53)(56,59)
(57,58)(61,64)(62,63);;
s3 := ( 5, 6)( 7, 9)(10,16)(11,15)(12,19)(13,18)(14,17)(20,21)(22,24)(25,31)
(26,30)(27,34)(28,33)(29,32)(35,51)(36,50)(37,54)(38,53)(39,52)(40,61)(41,60)
(42,64)(43,63)(44,62)(45,56)(46,55)(47,59)(48,58)(49,57);;
s4 := ( 5,40)( 6,41)( 7,42)( 8,43)( 9,44)(10,35)(11,36)(12,37)(13,38)(14,39)
(15,45)(16,46)(17,47)(18,48)(19,49)(20,55)(21,56)(22,57)(23,58)(24,59)(25,50)
(26,51)(27,52)(28,53)(29,54)(30,60)(31,61)(32,62)(33,63)(34,64);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(64)!(2,3);
s1 := Sym(64)!(1,2)(3,4);
s2 := Sym(64)!( 6, 9)( 7, 8)(11,14)(12,13)(16,19)(17,18)(21,24)(22,23)(26,29)
(27,28)(31,34)(32,33)(36,39)(37,38)(41,44)(42,43)(46,49)(47,48)(51,54)(52,53)
(56,59)(57,58)(61,64)(62,63);
s3 := Sym(64)!( 5, 6)( 7, 9)(10,16)(11,15)(12,19)(13,18)(14,17)(20,21)(22,24)
(25,31)(26,30)(27,34)(28,33)(29,32)(35,51)(36,50)(37,54)(38,53)(39,52)(40,61)
(41,60)(42,64)(43,63)(44,62)(45,56)(46,55)(47,59)(48,58)(49,57);
s4 := Sym(64)!( 5,40)( 6,41)( 7,42)( 8,43)( 9,44)(10,35)(11,36)(12,37)(13,38)
(14,39)(15,45)(16,46)(17,47)(18,48)(19,49)(20,55)(21,56)(22,57)(23,58)(24,59)
(25,50)(26,51)(27,52)(28,53)(29,54)(30,60)(31,61)(32,62)(33,63)(34,64);
poly := sub<Sym(64)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, 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*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope