Polytope of Type {2,2,4,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,6,3}*1728a
if this polytope has a name.
Group : SmallGroup(1728,30882)
Rank : 6
Schlafli Type : {2,2,4,6,3}
Number of vertices, edges, etc : 2, 2, 4, 36, 27, 9
Order of s0s1s2s3s4s5 : 12
Order of s0s1s2s3s4s5s4s3s2s1 : 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 : {2,2,2,6,3}*864
3-fold quotients : {2,2,4,6,3}*576
6-fold quotients : {2,2,2,6,3}*288
9-fold quotients : {2,2,4,2,3}*192
18-fold quotients : {2,2,2,2,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 59)( 6, 60)( 7, 61)( 8, 62)( 9, 63)( 10, 64)( 11, 65)( 12, 66)
( 13, 67)( 14, 68)( 15, 69)( 16, 70)( 17, 71)( 18, 72)( 19, 73)( 20, 74)
( 21, 75)( 22, 76)( 23, 77)( 24, 78)( 25, 79)( 26, 80)( 27, 81)( 28, 82)
( 29, 83)( 30, 84)( 31, 85)( 32, 86)( 33, 87)( 34, 88)( 35, 89)( 36, 90)
( 37, 91)( 38, 92)( 39, 93)( 40, 94)( 41, 95)( 42, 96)( 43, 97)( 44, 98)
( 45, 99)( 46,100)( 47,101)( 48,102)( 49,103)( 50,104)( 51,105)( 52,106)
( 53,107)( 54,108)( 55,109)( 56,110)( 57,111)( 58,112);;
s3 := ( 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);;
s4 := ( 5, 8)( 6, 9)( 7, 10)( 14, 26)( 15, 27)( 16, 28)( 17, 23)( 18, 24)
( 19, 25)( 20, 29)( 21, 30)( 22, 31)( 32, 35)( 33, 36)( 34, 37)( 41, 53)
( 42, 54)( 43, 55)( 44, 50)( 45, 51)( 46, 52)( 47, 56)( 48, 57)( 49, 58)
( 59, 62)( 60, 63)( 61, 64)( 68, 80)( 69, 81)( 70, 82)( 71, 77)( 72, 78)
( 73, 79)( 74, 83)( 75, 84)( 76, 85)( 86, 89)( 87, 90)( 88, 91)( 95,107)
( 96,108)( 97,109)( 98,104)( 99,105)(100,106)(101,110)(102,111)(103,112);;
s5 := ( 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,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(112)!(1,2);
s1 := Sym(112)!(3,4);
s2 := Sym(112)!( 5, 59)( 6, 60)( 7, 61)( 8, 62)( 9, 63)( 10, 64)( 11, 65)
( 12, 66)( 13, 67)( 14, 68)( 15, 69)( 16, 70)( 17, 71)( 18, 72)( 19, 73)
( 20, 74)( 21, 75)( 22, 76)( 23, 77)( 24, 78)( 25, 79)( 26, 80)( 27, 81)
( 28, 82)( 29, 83)( 30, 84)( 31, 85)( 32, 86)( 33, 87)( 34, 88)( 35, 89)
( 36, 90)( 37, 91)( 38, 92)( 39, 93)( 40, 94)( 41, 95)( 42, 96)( 43, 97)
( 44, 98)( 45, 99)( 46,100)( 47,101)( 48,102)( 49,103)( 50,104)( 51,105)
( 52,106)( 53,107)( 54,108)( 55,109)( 56,110)( 57,111)( 58,112);
s3 := 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);
s4 := Sym(112)!( 5, 8)( 6, 9)( 7, 10)( 14, 26)( 15, 27)( 16, 28)( 17, 23)
( 18, 24)( 19, 25)( 20, 29)( 21, 30)( 22, 31)( 32, 35)( 33, 36)( 34, 37)
( 41, 53)( 42, 54)( 43, 55)( 44, 50)( 45, 51)( 46, 52)( 47, 56)( 48, 57)
( 49, 58)( 59, 62)( 60, 63)( 61, 64)( 68, 80)( 69, 81)( 70, 82)( 71, 77)
( 72, 78)( 73, 79)( 74, 83)( 75, 84)( 76, 85)( 86, 89)( 87, 90)( 88, 91)
( 95,107)( 96,108)( 97,109)( 98,104)( 99,105)(100,106)(101,110)(102,111)
(103,112);
s5 := 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,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, 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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4*s3*s5*s4 >;
to this polytope