Polytope of Type {12,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12,2}*1728k
if this polytope has a name.
Group : SmallGroup(1728,47234)
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 : {12,6,2}*864i
   3-fold quotients : {4,12,2}*576
   4-fold quotients : {12,6,2}*432c
   6-fold quotients : {4,6,2}*288
   9-fold quotients : {12,4,2}*192a
   12-fold quotients : {4,6,2}*144
   18-fold quotients : {12,2,2}*96, {6,4,2}*96a
   27-fold quotients : {4,4,2}*64
   36-fold quotients : {6,2,2}*48
   54-fold quotients : {2,4,2}*32, {4,2,2}*32
   72-fold quotients : {3,2,2}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope