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Polytope of Type {8,30,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,30,2}*960
if this polytope has a name.
Group : SmallGroup(960,10708)
Rank : 4
Schlafli Type : {8,30,2}
Number of vertices, edges, etc : 8, 120, 30, 2
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,30,2,2} of size 1920
Vertex Figure Of :
   {2,8,30,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,30,2}*480a
   3-fold quotients : {8,10,2}*320
   4-fold quotients : {2,30,2}*240
   5-fold quotients : {8,6,2}*192
   6-fold quotients : {4,10,2}*160
   8-fold quotients : {2,15,2}*120
   10-fold quotients : {4,6,2}*96a
   12-fold quotients : {2,10,2}*80
   15-fold quotients : {8,2,2}*64
   20-fold quotients : {2,6,2}*48
   24-fold quotients : {2,5,2}*40
   30-fold quotients : {4,2,2}*32
   40-fold quotients : {2,3,2}*24
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,60,2}*1920a, {8,30,4}*1920a, {16,30,2}*1920
Permutation Representation (GAP) :
s0 := ( 31, 46)( 32, 47)( 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)( 61, 91)
( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68, 98)( 69, 99)
( 70,100)( 71,101)( 72,102)( 73,103)( 74,104)( 75,105)( 76,106)( 77,107)
( 78,108)( 79,109)( 80,110)( 81,111)( 82,112)( 83,113)( 84,114)( 85,115)
( 86,116)( 87,117)( 88,118)( 89,119)( 90,120);;
s1 := (  1, 61)(  2, 65)(  3, 64)(  4, 63)(  5, 62)(  6, 71)(  7, 75)(  8, 74)
(  9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)( 16, 76)
( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 86)( 22, 90)( 23, 89)( 24, 88)
( 25, 87)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31,106)( 32,110)
( 33,109)( 34,108)( 35,107)( 36,116)( 37,120)( 38,119)( 39,118)( 40,117)
( 41,111)( 42,115)( 43,114)( 44,113)( 45,112)( 46, 91)( 47, 95)( 48, 94)
( 49, 93)( 50, 92)( 51,101)( 52,105)( 53,104)( 54,103)( 55,102)( 56, 96)
( 57,100)( 58, 99)( 59, 98)( 60, 97);;
s2 := (  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)( 48, 55)
( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 67)( 62, 66)( 63, 70)( 64, 69)
( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)( 80, 83)
( 86, 87)( 88, 90)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)(101,102)
(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)(118,120);;
s3 := (121,122);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(122)!( 31, 46)( 32, 47)( 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)
( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68, 98)
( 69, 99)( 70,100)( 71,101)( 72,102)( 73,103)( 74,104)( 75,105)( 76,106)
( 77,107)( 78,108)( 79,109)( 80,110)( 81,111)( 82,112)( 83,113)( 84,114)
( 85,115)( 86,116)( 87,117)( 88,118)( 89,119)( 90,120);
s1 := Sym(122)!(  1, 61)(  2, 65)(  3, 64)(  4, 63)(  5, 62)(  6, 71)(  7, 75)
(  8, 74)(  9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)
( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 86)( 22, 90)( 23, 89)
( 24, 88)( 25, 87)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31,106)
( 32,110)( 33,109)( 34,108)( 35,107)( 36,116)( 37,120)( 38,119)( 39,118)
( 40,117)( 41,111)( 42,115)( 43,114)( 44,113)( 45,112)( 46, 91)( 47, 95)
( 48, 94)( 49, 93)( 50, 92)( 51,101)( 52,105)( 53,104)( 54,103)( 55,102)
( 56, 96)( 57,100)( 58, 99)( 59, 98)( 60, 97);
s2 := Sym(122)!(  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)
( 32, 36)( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 67)( 62, 66)( 63, 70)
( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 87)( 88, 90)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)
(101,102)(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)
(118,120);
s3 := Sym(122)!(121,122);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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