Polytope of Type {60,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,2,6}*1440
if this polytope has a name.
Group : SmallGroup(1440,5676)
Rank : 4
Schlafli Type : {60,2,6}
Number of vertices, edges, etc : 60, 60, 6, 6
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 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 : {60,2,3}*720, {30,2,6}*720
   3-fold quotients : {20,2,6}*480, {60,2,2}*480
   4-fold quotients : {15,2,6}*360, {30,2,3}*360
   5-fold quotients : {12,2,6}*288
   6-fold quotients : {20,2,3}*240, {10,2,6}*240, {30,2,2}*240
   8-fold quotients : {15,2,3}*180
   9-fold quotients : {20,2,2}*160
   10-fold quotients : {12,2,3}*144, {6,2,6}*144
   12-fold quotients : {5,2,6}*120, {10,2,3}*120, {15,2,2}*120
   15-fold quotients : {12,2,2}*96, {4,2,6}*96
   18-fold quotients : {10,2,2}*80
   20-fold quotients : {3,2,6}*72, {6,2,3}*72
   24-fold quotients : {5,2,3}*60
   30-fold quotients : {4,2,3}*48, {2,2,6}*48, {6,2,2}*48
   36-fold quotients : {5,2,2}*40
   40-fold quotients : {3,2,3}*36
   45-fold quotients : {4,2,2}*32
   60-fold quotients : {2,2,3}*24, {3,2,2}*24
   90-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 9,14)(10,13)(11,16)(12,15)(17,20)(18,19)(21,22)
(23,24)(25,26)(27,36)(28,35)(29,34)(30,33)(31,38)(32,37)(39,42)(40,41)(43,46)
(44,45)(47,48)(49,56)(50,55)(51,54)(52,53)(57,60)(58,59);;
s1 := ( 1,27)( 2,17)( 3,43)( 4,11)( 5,29)( 6, 9)( 7,49)( 8,33)(10,19)(12,39)
(13,25)(14,45)(15,23)(16,57)(18,31)(20,51)(21,28)(22,50)(24,35)(26,53)(30,41)
(32,40)(34,47)(36,59)(37,44)(38,58)(42,52)(46,55)(48,54)(56,60);;
s2 := (63,64)(65,66);;
s3 := (61,65)(62,63)(64,66);;
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*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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*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(66)!( 2, 3)( 4, 5)( 6, 7)( 9,14)(10,13)(11,16)(12,15)(17,20)(18,19)
(21,22)(23,24)(25,26)(27,36)(28,35)(29,34)(30,33)(31,38)(32,37)(39,42)(40,41)
(43,46)(44,45)(47,48)(49,56)(50,55)(51,54)(52,53)(57,60)(58,59);
s1 := Sym(66)!( 1,27)( 2,17)( 3,43)( 4,11)( 5,29)( 6, 9)( 7,49)( 8,33)(10,19)
(12,39)(13,25)(14,45)(15,23)(16,57)(18,31)(20,51)(21,28)(22,50)(24,35)(26,53)
(30,41)(32,40)(34,47)(36,59)(37,44)(38,58)(42,52)(46,55)(48,54)(56,60);
s2 := Sym(66)!(63,64)(65,66);
s3 := Sym(66)!(61,65)(62,63)(64,66);
poly := sub<Sym(66)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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*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