Polytope of Type {2,12,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,12}*1728d
if this polytope has a name.
Group : SmallGroup(1728,30413)
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 : {2,12,6}*864e
   3-fold quotients : {2,4,12}*576
   4-fold quotients : {2,12,6}*432b
   6-fold quotients : {2,4,6}*288
   12-fold quotients : {2,4,6}*144
   27-fold quotients : {2,4,4}*64
   54-fold quotients : {2,2,4}*32, {2,4,2}*32
   108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope