Polytope of Type {20,6,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,6,2,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,208127)
Rank : 5
Schlafli Type : {20,6,2,4}
Number of vertices, edges, etc : 20, 60, 6, 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 : {20,6,2,2}*960a, {10,6,2,4}*960
   3-fold quotients : {20,2,2,4}*640
   4-fold quotients : {10,6,2,2}*480
   5-fold quotients : {4,6,2,4}*384a
   6-fold quotients : {20,2,2,2}*320, {10,2,2,4}*320
   10-fold quotients : {2,6,2,4}*192, {4,6,2,2}*192a
   12-fold quotients : {5,2,2,4}*160, {10,2,2,2}*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 : {5,2,2,2}*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 := ( 2, 5)( 3, 4)( 7,10)( 8, 9)(12,15)(13,14)(17,20)(18,19)(22,25)(23,24)
(27,30)(28,29)(31,46)(32,50)(33,49)(34,48)(35,47)(36,51)(37,55)(38,54)(39,53)
(40,52)(41,56)(42,60)(43,59)(44,58)(45,57);;
s1 := ( 1,32)( 2,31)( 3,35)( 4,34)( 5,33)( 6,42)( 7,41)( 8,45)( 9,44)(10,43)
(11,37)(12,36)(13,40)(14,39)(15,38)(16,47)(17,46)(18,50)(19,49)(20,48)(21,57)
(22,56)(23,60)(24,59)(25,58)(26,52)(27,51)(28,55)(29,54)(30,53);;
s2 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5,10)(16,21)(17,22)(18,23)(19,24)(20,25)
(31,36)(32,37)(33,38)(34,39)(35,40)(46,51)(47,52)(48,53)(49,54)(50,55);;
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*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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope