Polytope of Type {2,6,30}

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

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

Permutation Representation (Magma) :

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

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