Polytope of Type {2,12,12}

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

to this polytope