Polytope of Type {2,30,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,6}*960
if this polytope has a name.
Group : SmallGroup(960,11372)
Rank : 4
Schlafli Type : {2,30,6}
Number of vertices, edges, etc : 2, 40, 120, 8
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,30,6,2} of size 1920
Vertex Figure Of :
   {2,2,30,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,15,6}*480
   5-fold quotients : {2,6,6}*192
   10-fold quotients : {2,3,6}*96, {2,6,3}*96
   12-fold quotients : {2,10,2}*80
   20-fold quotients : {2,3,3}*48
   24-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,60,6}*1920a, {4,30,6}*1920, {2,30,12}*1920a, {2,30,6}*1920, {2,60,6}*1920b, {2,30,12}*1920b
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  7, 19)(  8, 21)(  9, 20)( 10, 22)( 11, 15)( 12, 17)( 13, 16)
( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)( 29, 60)
( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)( 37, 52)
( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)( 68, 81)
( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)( 84,105)
( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)( 92,117)
( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)(100,109)
(101,108)(102,110);;
s2 := (  3, 87)(  4, 88)(  5, 90)(  6, 89)(  7, 83)(  8, 84)(  9, 86)( 10, 85)
( 11, 99)( 12,100)( 13,102)( 14,101)( 15, 95)( 16, 96)( 17, 98)( 18, 97)
( 19, 91)( 20, 92)( 21, 94)( 22, 93)( 23, 67)( 24, 68)( 25, 70)( 26, 69)
( 27, 63)( 28, 64)( 29, 66)( 30, 65)( 31, 79)( 32, 80)( 33, 82)( 34, 81)
( 35, 75)( 36, 76)( 37, 78)( 38, 77)( 39, 71)( 40, 72)( 41, 74)( 42, 73)
( 43,107)( 44,108)( 45,110)( 46,109)( 47,103)( 48,104)( 49,106)( 50,105)
( 51,119)( 52,120)( 53,122)( 54,121)( 55,115)( 56,116)( 57,118)( 58,117)
( 59,111)( 60,112)( 61,114)( 62,113);;
s3 := (  3,  6)(  7, 10)( 11, 14)( 15, 18)( 19, 22)( 23, 46)( 24, 44)( 25, 45)
( 26, 43)( 27, 50)( 28, 48)( 29, 49)( 30, 47)( 31, 54)( 32, 52)( 33, 53)
( 34, 51)( 35, 58)( 36, 56)( 37, 57)( 38, 55)( 39, 62)( 40, 60)( 41, 61)
( 42, 59)( 63, 66)( 67, 70)( 71, 74)( 75, 78)( 79, 82)( 83,106)( 84,104)
( 85,105)( 86,103)( 87,110)( 88,108)( 89,109)( 90,107)( 91,114)( 92,112)
( 93,113)( 94,111)( 95,118)( 96,116)( 97,117)( 98,115)( 99,122)(100,120)
(101,121)(102,119);;
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*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(122)!(1,2);
s1 := Sym(122)!(  4,  5)(  7, 19)(  8, 21)(  9, 20)( 10, 22)( 11, 15)( 12, 17)
( 13, 16)( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)
( 29, 60)( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)
( 37, 52)( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)
( 68, 81)( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)
( 84,105)( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)
( 92,117)( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)
(100,109)(101,108)(102,110);
s2 := Sym(122)!(  3, 87)(  4, 88)(  5, 90)(  6, 89)(  7, 83)(  8, 84)(  9, 86)
( 10, 85)( 11, 99)( 12,100)( 13,102)( 14,101)( 15, 95)( 16, 96)( 17, 98)
( 18, 97)( 19, 91)( 20, 92)( 21, 94)( 22, 93)( 23, 67)( 24, 68)( 25, 70)
( 26, 69)( 27, 63)( 28, 64)( 29, 66)( 30, 65)( 31, 79)( 32, 80)( 33, 82)
( 34, 81)( 35, 75)( 36, 76)( 37, 78)( 38, 77)( 39, 71)( 40, 72)( 41, 74)
( 42, 73)( 43,107)( 44,108)( 45,110)( 46,109)( 47,103)( 48,104)( 49,106)
( 50,105)( 51,119)( 52,120)( 53,122)( 54,121)( 55,115)( 56,116)( 57,118)
( 58,117)( 59,111)( 60,112)( 61,114)( 62,113);
s3 := Sym(122)!(  3,  6)(  7, 10)( 11, 14)( 15, 18)( 19, 22)( 23, 46)( 24, 44)
( 25, 45)( 26, 43)( 27, 50)( 28, 48)( 29, 49)( 30, 47)( 31, 54)( 32, 52)
( 33, 53)( 34, 51)( 35, 58)( 36, 56)( 37, 57)( 38, 55)( 39, 62)( 40, 60)
( 41, 61)( 42, 59)( 63, 66)( 67, 70)( 71, 74)( 75, 78)( 79, 82)( 83,106)
( 84,104)( 85,105)( 86,103)( 87,110)( 88,108)( 89,109)( 90,107)( 91,114)
( 92,112)( 93,113)( 94,111)( 95,118)( 96,116)( 97,117)( 98,115)( 99,122)
(100,120)(101,121)(102,119);
poly := sub<Sym(122)|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*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s3 >;

to this polytope