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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,4,30}*1920a
if this polytope has a name.
Group : SmallGroup(1920,208100)
Rank : 5
Schlafli Type : {4,2,4,30}
Number of vertices, edges, etc : 4, 4, 4, 60, 30
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 : {2,2,4,30}*960a, {4,2,2,30}*960
   3-fold quotients : {4,2,4,10}*640
   4-fold quotients : {4,2,2,15}*480, {2,2,2,30}*480
   5-fold quotients : {4,2,4,6}*384a
   6-fold quotients : {2,2,4,10}*320, {4,2,2,10}*320
   8-fold quotients : {2,2,2,15}*240
   10-fold quotients : {2,2,4,6}*192a, {4,2,2,6}*192
   12-fold quotients : {4,2,2,5}*160, {2,2,2,10}*160
   15-fold quotients : {4,2,4,2}*128
   20-fold quotients : {4,2,2,3}*96, {2,2,2,6}*96
   24-fold quotients : {2,2,2,5}*80
   30-fold quotients : {2,2,4,2}*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 := (35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)
(45,60)(46,61)(47,62)(48,63)(49,64);;
s3 := ( 5,35)( 6,39)( 7,38)( 8,37)( 9,36)(10,45)(11,49)(12,48)(13,47)(14,46)
(15,40)(16,44)(17,43)(18,42)(19,41)(20,50)(21,54)(22,53)(23,52)(24,51)(25,60)
(26,64)(27,63)(28,62)(29,61)(30,55)(31,59)(32,58)(33,57)(34,56);;
s4 := ( 5,11)( 6,10)( 7,14)( 8,13)( 9,12)(15,16)(17,19)(20,26)(21,25)(22,29)
(23,28)(24,27)(30,31)(32,34)(35,41)(36,40)(37,44)(38,43)(39,42)(45,46)(47,49)
(50,56)(51,55)(52,59)(53,58)(54,57)(60,61)(62,64);;
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*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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)!(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)
(44,59)(45,60)(46,61)(47,62)(48,63)(49,64);
s3 := Sym(64)!( 5,35)( 6,39)( 7,38)( 8,37)( 9,36)(10,45)(11,49)(12,48)(13,47)
(14,46)(15,40)(16,44)(17,43)(18,42)(19,41)(20,50)(21,54)(22,53)(23,52)(24,51)
(25,60)(26,64)(27,63)(28,62)(29,61)(30,55)(31,59)(32,58)(33,57)(34,56);
s4 := Sym(64)!( 5,11)( 6,10)( 7,14)( 8,13)( 9,12)(15,16)(17,19)(20,26)(21,25)
(22,29)(23,28)(24,27)(30,31)(32,34)(35,41)(36,40)(37,44)(38,43)(39,42)(45,46)
(47,49)(50,56)(51,55)(52,59)(53,58)(54,57)(60,61)(62,64);
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*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*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*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*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