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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,12,6}*1728c
if this polytope has a name.
Group : SmallGroup(1728,30882)
Rank : 5
Schlafli Type : {2,2,12,6}
Number of vertices, edges, etc : 2, 2, 36, 108, 18
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 : {2,2,6,6}*864a
   3-fold quotients : {2,2,12,6}*576c
   4-fold quotients : {2,2,6,3}*432
   6-fold quotients : {2,2,6,6}*288b
   9-fold quotients : {2,2,4,6}*192a
   12-fold quotients : {2,2,6,3}*144
   18-fold quotients : {2,2,2,6}*96
   27-fold quotients : {2,2,4,2}*64
   36-fold quotients : {2,2,2,3}*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 := (3,4);;
s2 := (  6,  7)(  8, 11)(  9, 13)( 10, 12)( 15, 16)( 17, 20)( 18, 22)( 19, 21)
( 24, 25)( 26, 29)( 27, 31)( 28, 30)( 33, 34)( 35, 38)( 36, 40)( 37, 39)
( 42, 43)( 44, 47)( 45, 49)( 46, 48)( 51, 52)( 53, 56)( 54, 58)( 55, 57)
( 59, 86)( 60, 88)( 61, 87)( 62, 92)( 63, 94)( 64, 93)( 65, 89)( 66, 91)
( 67, 90)( 68, 95)( 69, 97)( 70, 96)( 71,101)( 72,103)( 73,102)( 74, 98)
( 75,100)( 76, 99)( 77,104)( 78,106)( 79,105)( 80,110)( 81,112)( 82,111)
( 83,107)( 84,109)( 85,108);;
s3 := (  5, 62)(  6, 63)(  7, 64)(  8, 59)(  9, 60)( 10, 61)( 11, 65)( 12, 66)
( 13, 67)( 14, 80)( 15, 81)( 16, 82)( 17, 77)( 18, 78)( 19, 79)( 20, 83)
( 21, 84)( 22, 85)( 23, 71)( 24, 72)( 25, 73)( 26, 68)( 27, 69)( 28, 70)
( 29, 74)( 30, 75)( 31, 76)( 32, 89)( 33, 90)( 34, 91)( 35, 86)( 36, 87)
( 37, 88)( 38, 92)( 39, 93)( 40, 94)( 41,107)( 42,108)( 43,109)( 44,104)
( 45,105)( 46,106)( 47,110)( 48,111)( 49,112)( 50, 98)( 51, 99)( 52,100)
( 53, 95)( 54, 96)( 55, 97)( 56,101)( 57,102)( 58,103);;
s4 := (  5, 14)(  6, 15)(  7, 16)(  8, 22)(  9, 20)( 10, 21)( 11, 18)( 12, 19)
( 13, 17)( 26, 31)( 27, 29)( 28, 30)( 32, 41)( 33, 42)( 34, 43)( 35, 49)
( 36, 47)( 37, 48)( 38, 45)( 39, 46)( 40, 44)( 53, 58)( 54, 56)( 55, 57)
( 59, 68)( 60, 69)( 61, 70)( 62, 76)( 63, 74)( 64, 75)( 65, 72)( 66, 73)
( 67, 71)( 80, 85)( 81, 83)( 82, 84)( 86, 95)( 87, 96)( 88, 97)( 89,103)
( 90,101)( 91,102)( 92, 99)( 93,100)( 94, 98)(107,112)(108,110)(109,111);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s4*s3*s2*s3*s4*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s2*s3*s4*s3*s2*s3*s4*s2*s3*s2*s3*s4*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(112)!(1,2);
s1 := Sym(112)!(3,4);
s2 := Sym(112)!(  6,  7)(  8, 11)(  9, 13)( 10, 12)( 15, 16)( 17, 20)( 18, 22)
( 19, 21)( 24, 25)( 26, 29)( 27, 31)( 28, 30)( 33, 34)( 35, 38)( 36, 40)
( 37, 39)( 42, 43)( 44, 47)( 45, 49)( 46, 48)( 51, 52)( 53, 56)( 54, 58)
( 55, 57)( 59, 86)( 60, 88)( 61, 87)( 62, 92)( 63, 94)( 64, 93)( 65, 89)
( 66, 91)( 67, 90)( 68, 95)( 69, 97)( 70, 96)( 71,101)( 72,103)( 73,102)
( 74, 98)( 75,100)( 76, 99)( 77,104)( 78,106)( 79,105)( 80,110)( 81,112)
( 82,111)( 83,107)( 84,109)( 85,108);
s3 := Sym(112)!(  5, 62)(  6, 63)(  7, 64)(  8, 59)(  9, 60)( 10, 61)( 11, 65)
( 12, 66)( 13, 67)( 14, 80)( 15, 81)( 16, 82)( 17, 77)( 18, 78)( 19, 79)
( 20, 83)( 21, 84)( 22, 85)( 23, 71)( 24, 72)( 25, 73)( 26, 68)( 27, 69)
( 28, 70)( 29, 74)( 30, 75)( 31, 76)( 32, 89)( 33, 90)( 34, 91)( 35, 86)
( 36, 87)( 37, 88)( 38, 92)( 39, 93)( 40, 94)( 41,107)( 42,108)( 43,109)
( 44,104)( 45,105)( 46,106)( 47,110)( 48,111)( 49,112)( 50, 98)( 51, 99)
( 52,100)( 53, 95)( 54, 96)( 55, 97)( 56,101)( 57,102)( 58,103);
s4 := Sym(112)!(  5, 14)(  6, 15)(  7, 16)(  8, 22)(  9, 20)( 10, 21)( 11, 18)
( 12, 19)( 13, 17)( 26, 31)( 27, 29)( 28, 30)( 32, 41)( 33, 42)( 34, 43)
( 35, 49)( 36, 47)( 37, 48)( 38, 45)( 39, 46)( 40, 44)( 53, 58)( 54, 56)
( 55, 57)( 59, 68)( 60, 69)( 61, 70)( 62, 76)( 63, 74)( 64, 75)( 65, 72)
( 66, 73)( 67, 71)( 80, 85)( 81, 83)( 82, 84)( 86, 95)( 87, 96)( 88, 97)
( 89,103)( 90,101)( 91,102)( 92, 99)( 93,100)( 94, 98)(107,112)(108,110)
(109,111);
poly := sub<Sym(112)|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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s4*s3*s2*s3*s4*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s2*s3*s4*s3*s2*s3*s4*s2*s3*s2*s3*s4*s3*s2*s3 >;

to this polytope