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Polytope of Type {2,3,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,4,10}*960
if this polytope has a name.
Group : SmallGroup(960,11372)
Rank : 5
Schlafli Type : {2,3,4,10}
Number of vertices, edges, etc : 2, 6, 12, 40, 10
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,3,4,10,2} of size 1920
Vertex Figure Of :
   {2,2,3,4,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
   4-fold quotients : {2,3,2,10}*240
   5-fold quotients : {2,3,4,2}*192
   8-fold quotients : {2,3,2,5}*120
   10-fold quotients : {2,3,4,2}*96
   20-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,3,4,20}*1920, {2,3,8,10}*1920, {2,6,4,10}*1920
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, 27)(  8, 28)(  9, 30)( 10, 29)
( 11, 31)( 12, 32)( 13, 34)( 14, 33)( 15, 35)( 16, 36)( 17, 38)( 18, 37)
( 19, 39)( 20, 40)( 21, 42)( 22, 41)( 45, 46)( 49, 50)( 53, 54)( 57, 58)
( 61, 62)( 63, 83)( 64, 84)( 65, 86)( 66, 85)( 67, 87)( 68, 88)( 69, 90)
( 70, 89)( 71, 91)( 72, 92)( 73, 94)( 74, 93)( 75, 95)( 76, 96)( 77, 98)
( 78, 97)( 79, 99)( 80,100)( 81,102)( 82,101)(105,106)(109,110)(113,114)
(117,118)(121,122);;
s3 := (  3,  6)(  4,  5)(  7, 22)(  8, 21)(  9, 20)( 10, 19)( 11, 18)( 12, 17)
( 13, 16)( 14, 15)( 23, 26)( 24, 25)( 27, 42)( 28, 41)( 29, 40)( 30, 39)
( 31, 38)( 32, 37)( 33, 36)( 34, 35)( 43, 46)( 44, 45)( 47, 62)( 48, 61)
( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 54, 55)( 63, 66)( 64, 65)
( 67, 82)( 68, 81)( 69, 80)( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)
( 83, 86)( 84, 85)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)
( 93, 96)( 94, 95)(103,106)(104,105)(107,122)(108,121)(109,120)(110,119)
(111,118)(112,117)(113,116)(114,115);;
s4 := (  3, 67)(  4, 68)(  5, 69)(  6, 70)(  7, 63)(  8, 64)(  9, 65)( 10, 66)
( 11, 79)( 12, 80)( 13, 81)( 14, 82)( 15, 75)( 16, 76)( 17, 77)( 18, 78)
( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 87)( 24, 88)( 25, 89)( 26, 90)
( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 99)( 32,100)( 33,101)( 34,102)
( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 91)( 40, 92)( 41, 93)( 42, 94)
( 43,107)( 44,108)( 45,109)( 46,110)( 47,103)( 48,104)( 49,105)( 50,106)
( 51,119)( 52,120)( 53,121)( 54,122)( 55,115)( 56,116)( 57,117)( 58,118)
( 59,111)( 60,112)( 61,113)( 62,114);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
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, 27)(  8, 28)(  9, 30)
( 10, 29)( 11, 31)( 12, 32)( 13, 34)( 14, 33)( 15, 35)( 16, 36)( 17, 38)
( 18, 37)( 19, 39)( 20, 40)( 21, 42)( 22, 41)( 45, 46)( 49, 50)( 53, 54)
( 57, 58)( 61, 62)( 63, 83)( 64, 84)( 65, 86)( 66, 85)( 67, 87)( 68, 88)
( 69, 90)( 70, 89)( 71, 91)( 72, 92)( 73, 94)( 74, 93)( 75, 95)( 76, 96)
( 77, 98)( 78, 97)( 79, 99)( 80,100)( 81,102)( 82,101)(105,106)(109,110)
(113,114)(117,118)(121,122);
s3 := Sym(122)!(  3,  6)(  4,  5)(  7, 22)(  8, 21)(  9, 20)( 10, 19)( 11, 18)
( 12, 17)( 13, 16)( 14, 15)( 23, 26)( 24, 25)( 27, 42)( 28, 41)( 29, 40)
( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 34, 35)( 43, 46)( 44, 45)( 47, 62)
( 48, 61)( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 54, 55)( 63, 66)
( 64, 65)( 67, 82)( 68, 81)( 69, 80)( 70, 79)( 71, 78)( 72, 77)( 73, 76)
( 74, 75)( 83, 86)( 84, 85)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)
( 92, 97)( 93, 96)( 94, 95)(103,106)(104,105)(107,122)(108,121)(109,120)
(110,119)(111,118)(112,117)(113,116)(114,115);
s4 := Sym(122)!(  3, 67)(  4, 68)(  5, 69)(  6, 70)(  7, 63)(  8, 64)(  9, 65)
( 10, 66)( 11, 79)( 12, 80)( 13, 81)( 14, 82)( 15, 75)( 16, 76)( 17, 77)
( 18, 78)( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 87)( 24, 88)( 25, 89)
( 26, 90)( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 99)( 32,100)( 33,101)
( 34,102)( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 91)( 40, 92)( 41, 93)
( 42, 94)( 43,107)( 44,108)( 45,109)( 46,110)( 47,103)( 48,104)( 49,105)
( 50,106)( 51,119)( 52,120)( 53,121)( 54,122)( 55,115)( 56,116)( 57,117)
( 58,118)( 59,111)( 60,112)( 61,113)( 62,114);
poly := sub<Sym(122)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

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