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Polytope of Type {2,8,30}

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

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