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Polytope of Type {2,12,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,6,6}*1728c
if this polytope has a name.
Group : SmallGroup(1728,47319)
Rank : 5
Schlafli Type : {2,12,6,6}
Number of vertices, edges, etc : 2, 12, 36, 18, 6
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,6,6}*864e
   3-fold quotients : {2,12,6,2}*576a, {2,4,6,6}*576b
   6-fold quotients : {2,2,6,6}*288c, {2,6,6,2}*288a
   9-fold quotients : {2,12,2,2}*192, {2,4,6,2}*192a
   12-fold quotients : {2,2,3,6}*144
   18-fold quotients : {2,2,6,2}*96, {2,6,2,2}*96
   27-fold quotients : {2,4,2,2}*64
   36-fold quotients : {2,2,3,2}*48, {2,3,2,2}*48
   54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)( 17, 26)( 18, 27)( 19, 28)
( 20, 29)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)( 45, 54)
( 46, 55)( 47, 56)( 57, 84)( 58, 85)( 59, 86)( 60, 87)( 61, 88)( 62, 89)
( 63, 90)( 64, 91)( 65, 92)( 66,102)( 67,103)( 68,104)( 69,105)( 70,106)
( 71,107)( 72,108)( 73,109)( 74,110)( 75, 93)( 76, 94)( 77, 95)( 78, 96)
( 79, 97)( 80, 98)( 81, 99)( 82,100)( 83,101);;
s2 := (  3, 66)(  4, 68)(  5, 67)(  6, 72)(  7, 74)(  8, 73)(  9, 69)( 10, 71)
( 11, 70)( 12, 57)( 13, 59)( 14, 58)( 15, 63)( 16, 65)( 17, 64)( 18, 60)
( 19, 62)( 20, 61)( 21, 75)( 22, 77)( 23, 76)( 24, 81)( 25, 83)( 26, 82)
( 27, 78)( 28, 80)( 29, 79)( 30, 93)( 31, 95)( 32, 94)( 33, 99)( 34,101)
( 35,100)( 36, 96)( 37, 98)( 38, 97)( 39, 84)( 40, 86)( 41, 85)( 42, 90)
( 43, 92)( 44, 91)( 45, 87)( 46, 89)( 47, 88)( 48,102)( 49,104)( 50,103)
( 51,108)( 52,110)( 53,109)( 54,105)( 55,107)( 56,106);;
s3 := (  3,  7)(  4,  6)(  5,  8)(  9, 10)( 12, 16)( 13, 15)( 14, 17)( 18, 19)
( 21, 25)( 22, 24)( 23, 26)( 27, 28)( 30, 34)( 31, 33)( 32, 35)( 36, 37)
( 39, 43)( 40, 42)( 41, 44)( 45, 46)( 48, 52)( 49, 51)( 50, 53)( 54, 55)
( 57, 61)( 58, 60)( 59, 62)( 63, 64)( 66, 70)( 67, 69)( 68, 71)( 72, 73)
( 75, 79)( 76, 78)( 77, 80)( 81, 82)( 84, 88)( 85, 87)( 86, 89)( 90, 91)
( 93, 97)( 94, 96)( 95, 98)( 99,100)(102,106)(103,105)(104,107)(108,109);;
s4 := (  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)( 25, 26)
( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)( 49, 50)
( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)( 73, 74)
( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 94, 95)( 97, 98)
(100,101)(103,104)(106,107)(109,110);;
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*s3*s2*s1*s2*s3*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
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(110)!(1,2);
s1 := Sym(110)!( 12, 21)( 13, 22)( 14, 23)( 15, 24)( 16, 25)( 17, 26)( 18, 27)
( 19, 28)( 20, 29)( 39, 48)( 40, 49)( 41, 50)( 42, 51)( 43, 52)( 44, 53)
( 45, 54)( 46, 55)( 47, 56)( 57, 84)( 58, 85)( 59, 86)( 60, 87)( 61, 88)
( 62, 89)( 63, 90)( 64, 91)( 65, 92)( 66,102)( 67,103)( 68,104)( 69,105)
( 70,106)( 71,107)( 72,108)( 73,109)( 74,110)( 75, 93)( 76, 94)( 77, 95)
( 78, 96)( 79, 97)( 80, 98)( 81, 99)( 82,100)( 83,101);
s2 := Sym(110)!(  3, 66)(  4, 68)(  5, 67)(  6, 72)(  7, 74)(  8, 73)(  9, 69)
( 10, 71)( 11, 70)( 12, 57)( 13, 59)( 14, 58)( 15, 63)( 16, 65)( 17, 64)
( 18, 60)( 19, 62)( 20, 61)( 21, 75)( 22, 77)( 23, 76)( 24, 81)( 25, 83)
( 26, 82)( 27, 78)( 28, 80)( 29, 79)( 30, 93)( 31, 95)( 32, 94)( 33, 99)
( 34,101)( 35,100)( 36, 96)( 37, 98)( 38, 97)( 39, 84)( 40, 86)( 41, 85)
( 42, 90)( 43, 92)( 44, 91)( 45, 87)( 46, 89)( 47, 88)( 48,102)( 49,104)
( 50,103)( 51,108)( 52,110)( 53,109)( 54,105)( 55,107)( 56,106);
s3 := Sym(110)!(  3,  7)(  4,  6)(  5,  8)(  9, 10)( 12, 16)( 13, 15)( 14, 17)
( 18, 19)( 21, 25)( 22, 24)( 23, 26)( 27, 28)( 30, 34)( 31, 33)( 32, 35)
( 36, 37)( 39, 43)( 40, 42)( 41, 44)( 45, 46)( 48, 52)( 49, 51)( 50, 53)
( 54, 55)( 57, 61)( 58, 60)( 59, 62)( 63, 64)( 66, 70)( 67, 69)( 68, 71)
( 72, 73)( 75, 79)( 76, 78)( 77, 80)( 81, 82)( 84, 88)( 85, 87)( 86, 89)
( 90, 91)( 93, 97)( 94, 96)( 95, 98)( 99,100)(102,106)(103,105)(104,107)
(108,109);
s4 := Sym(110)!(  4,  5)(  7,  8)( 10, 11)( 13, 14)( 16, 17)( 19, 20)( 22, 23)
( 25, 26)( 28, 29)( 31, 32)( 34, 35)( 37, 38)( 40, 41)( 43, 44)( 46, 47)
( 49, 50)( 52, 53)( 55, 56)( 58, 59)( 61, 62)( 64, 65)( 67, 68)( 70, 71)
( 73, 74)( 76, 77)( 79, 80)( 82, 83)( 85, 86)( 88, 89)( 91, 92)( 94, 95)
( 97, 98)(100,101)(103,104)(106,107)(109,110);
poly := sub<Sym(110)|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*s3*s2*s1*s2*s3*s2, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
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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