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