Polytope of Type {2,4,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,30}*480a
if this polytope has a name.
Group : SmallGroup(480,1169)
Rank : 4
Schlafli Type : {2,4,30}
Number of vertices, edges, etc : 2, 4, 60, 30
Order of s₀s₁s₂s₃ : 60
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,30,2} of size 960
   {2,4,30,4} of size 1920
   {2,4,30,4} of size 1920
Vertex Figure Of :
   {2,2,4,30} of size 960
   {3,2,4,30} of size 1440
   {4,2,4,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,2,30}*240
   3-fold quotients : {2,4,10}*160
   4-fold quotients : {2,2,15}*120
   5-fold quotients : {2,4,6}*96a
   6-fold quotients : {2,2,10}*80
   10-fold quotients : {2,2,6}*48
   12-fold quotients : {2,2,5}*40
   15-fold quotients : {2,4,2}*32
   20-fold quotients : {2,2,3}*24
   30-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,4,60}*960a, {4,4,30}*960, {2,8,30}*960
   3-fold covers : {2,4,90}*1440a, {2,12,30}*1440b, {6,4,30}*1440, {2,12,30}*1440c
   4-fold covers : {4,4,60}*1920, {4,8,30}*1920a, {8,4,30}*1920a, {2,8,60}*1920a, {2,4,120}*1920a, {4,8,30}*1920b, {8,4,30}*1920b, {2,8,60}*1920b, {2,4,120}*1920b, {4,4,30}*1920a, {2,4,60}*1920a, {2,16,30}*1920, {2,4,30}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope