Polytope of Type {30,4,2,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4,2,2,2}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240411)
Rank : 6
Schlafli Type : {30,4,2,2,2}
Number of vertices, edges, etc : 30, 60, 4, 2, 2, 2
Order of s0s1s2s3s4s5 : 30
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {15,4,2,2,2}*960
5-fold quotients : {6,4,2,2,2}*384b
10-fold quotients : {3,4,2,2,2}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 17)( 6, 19)( 7, 18)( 8, 20)( 9, 13)( 10, 15)( 11, 14)
( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)( 27, 58)
( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)( 35, 50)
( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)( 66, 79)
( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)( 90,115)
( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)( 98,107)
( 99,106)(100,108);;
s1 := ( 1, 85)( 2, 86)( 3, 88)( 4, 87)( 5, 81)( 6, 82)( 7, 84)( 8, 83)
( 9, 97)( 10, 98)( 11,100)( 12, 99)( 13, 93)( 14, 94)( 15, 96)( 16, 95)
( 17, 89)( 18, 90)( 19, 92)( 20, 91)( 21, 65)( 22, 66)( 23, 68)( 24, 67)
( 25, 61)( 26, 62)( 27, 64)( 28, 63)( 29, 77)( 30, 78)( 31, 80)( 32, 79)
( 33, 73)( 34, 74)( 35, 76)( 36, 75)( 37, 69)( 38, 70)( 39, 72)( 40, 71)
( 41,105)( 42,106)( 43,108)( 44,107)( 45,101)( 46,102)( 47,104)( 48,103)
( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)( 56,115)
( 57,109)( 58,110)( 59,112)( 60,111);;
s2 := ( 1, 64)( 2, 63)( 3, 62)( 4, 61)( 5, 68)( 6, 67)( 7, 66)( 8, 65)
( 9, 72)( 10, 71)( 11, 70)( 12, 69)( 13, 76)( 14, 75)( 15, 74)( 16, 73)
( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 84)( 22, 83)( 23, 82)( 24, 81)
( 25, 88)( 26, 87)( 27, 86)( 28, 85)( 29, 92)( 30, 91)( 31, 90)( 32, 89)
( 33, 96)( 34, 95)( 35, 94)( 36, 93)( 37,100)( 38, 99)( 39, 98)( 40, 97)
( 41,104)( 42,103)( 43,102)( 44,101)( 45,108)( 46,107)( 47,106)( 48,105)
( 49,112)( 50,111)( 51,110)( 52,109)( 53,116)( 54,115)( 55,114)( 56,113)
( 57,120)( 58,119)( 59,118)( 60,117);;
s3 := (121,122);;
s4 := (123,124);;
s5 := (125,126);;
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(126)!( 2, 3)( 5, 17)( 6, 19)( 7, 18)( 8, 20)( 9, 13)( 10, 15)
( 11, 14)( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)
( 27, 58)( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)
( 35, 50)( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)
( 66, 79)( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)
( 82,103)( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)
( 90,115)( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)
( 98,107)( 99,106)(100,108);
s1 := Sym(126)!( 1, 85)( 2, 86)( 3, 88)( 4, 87)( 5, 81)( 6, 82)( 7, 84)
( 8, 83)( 9, 97)( 10, 98)( 11,100)( 12, 99)( 13, 93)( 14, 94)( 15, 96)
( 16, 95)( 17, 89)( 18, 90)( 19, 92)( 20, 91)( 21, 65)( 22, 66)( 23, 68)
( 24, 67)( 25, 61)( 26, 62)( 27, 64)( 28, 63)( 29, 77)( 30, 78)( 31, 80)
( 32, 79)( 33, 73)( 34, 74)( 35, 76)( 36, 75)( 37, 69)( 38, 70)( 39, 72)
( 40, 71)( 41,105)( 42,106)( 43,108)( 44,107)( 45,101)( 46,102)( 47,104)
( 48,103)( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)
( 56,115)( 57,109)( 58,110)( 59,112)( 60,111);
s2 := Sym(126)!( 1, 64)( 2, 63)( 3, 62)( 4, 61)( 5, 68)( 6, 67)( 7, 66)
( 8, 65)( 9, 72)( 10, 71)( 11, 70)( 12, 69)( 13, 76)( 14, 75)( 15, 74)
( 16, 73)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 84)( 22, 83)( 23, 82)
( 24, 81)( 25, 88)( 26, 87)( 27, 86)( 28, 85)( 29, 92)( 30, 91)( 31, 90)
( 32, 89)( 33, 96)( 34, 95)( 35, 94)( 36, 93)( 37,100)( 38, 99)( 39, 98)
( 40, 97)( 41,104)( 42,103)( 43,102)( 44,101)( 45,108)( 46,107)( 47,106)
( 48,105)( 49,112)( 50,111)( 51,110)( 52,109)( 53,116)( 54,115)( 55,114)
( 56,113)( 57,120)( 58,119)( 59,118)( 60,117);
s3 := Sym(126)!(121,122);
s4 := Sym(126)!(123,124);
s5 := Sym(126)!(125,126);
poly := sub<Sym(126)|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*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0 >;
to this polytope