Polytope of Type {2,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*1728l
if this polytope has a name.
Group : SmallGroup(1728,47234)
Rank : 4
Schlafli Type : {2,12,12}
Number of vertices, edges, etc : 2, 36, 216, 36
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 : {2,6,12}*864i
   3-fold quotients : {2,12,4}*576
   4-fold quotients : {2,6,12}*432c
   6-fold quotients : {2,6,4}*288
   9-fold quotients : {2,4,12}*192a
   12-fold quotients : {2,6,4}*144
   18-fold quotients : {2,2,12}*96, {2,4,6}*96a
   27-fold quotients : {2,4,4}*64
   36-fold quotients : {2,2,6}*48
   54-fold quotients : {2,2,4}*32, {2,4,2}*32
   72-fold quotients : {2,2,3}*24
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

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