Polytope of Type {12,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,2}*1728g
if this polytope has a name.
Group : SmallGroup(1728,30413)
Rank : 4
Schlafli Type : {12,12,2}
Number of vertices, edges, etc : 36, 216, 36, 2
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 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 : {6,12,2}*864e
   3-fold quotients : {12,4,2}*576
   4-fold quotients : {6,12,2}*432a
   6-fold quotients : {6,4,2}*288
   12-fold quotients : {6,4,2}*144
   27-fold quotients : {4,4,2}*64
   54-fold quotients : {2,4,2}*32, {4,2,2}*32
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope