Polytope of Type {4,30,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30,2,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,208100)
Rank : 5
Schlafli Type : {4,30,2,4}
Number of vertices, edges, etc : 4, 60, 30, 4, 4
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 : {2,30,2,4}*960, {4,30,2,2}*960a
   3-fold quotients : {4,10,2,4}*640
   4-fold quotients : {2,15,2,4}*480, {2,30,2,2}*480
   5-fold quotients : {4,6,2,4}*384a
   6-fold quotients : {2,10,2,4}*320, {4,10,2,2}*320
   8-fold quotients : {2,15,2,2}*240
   10-fold quotients : {2,6,2,4}*192, {4,6,2,2}*192a
   12-fold quotients : {2,5,2,4}*160, {2,10,2,2}*160
   15-fold quotients : {4,2,2,4}*128
   20-fold quotients : {2,3,2,4}*96, {2,6,2,2}*96
   24-fold quotients : {2,5,2,2}*80
   30-fold quotients : {2,2,2,4}*64, {4,2,2,2}*64
   40-fold quotients : {2,3,2,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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