Polytope of Type {3,2,4,30}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,4,30}*1440c
if this polytope has a name.
Group : SmallGroup(1440,5900)
Rank : 5
Schlafli Type : {3,2,4,30}
Number of vertices, edges, etc : 3, 3, 4, 60, 30
Order of s0s1s2s3s4 : 15
Order of s0s1s2s3s4s3s2s1 : 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 : {3,2,4,15}*720
5-fold quotients : {3,2,4,6}*288b
10-fold quotients : {3,2,4,3}*144
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4, 65)( 5, 64)( 6, 67)( 7, 66)( 8, 69)( 9, 68)( 10, 71)( 11, 70)
( 12, 73)( 13, 72)( 14, 75)( 15, 74)( 16, 77)( 17, 76)( 18, 79)( 19, 78)
( 20, 81)( 21, 80)( 22, 83)( 23, 82)( 24, 85)( 25, 84)( 26, 87)( 27, 86)
( 28, 89)( 29, 88)( 30, 91)( 31, 90)( 32, 93)( 33, 92)( 34, 95)( 35, 94)
( 36, 97)( 37, 96)( 38, 99)( 39, 98)( 40,101)( 41,100)( 42,103)( 43,102)
( 44,105)( 45,104)( 46,107)( 47,106)( 48,109)( 49,108)( 50,111)( 51,110)
( 52,113)( 53,112)( 54,115)( 55,114)( 56,117)( 57,116)( 58,119)( 59,118)
( 60,121)( 61,120)( 62,123)( 63,122);;
s3 := ( 5, 6)( 8, 20)( 9, 22)( 10, 21)( 11, 23)( 12, 16)( 13, 18)( 14, 17)
( 15, 19)( 24, 44)( 25, 46)( 26, 45)( 27, 47)( 28, 60)( 29, 62)( 30, 61)
( 31, 63)( 32, 56)( 33, 58)( 34, 57)( 35, 59)( 36, 52)( 37, 54)( 38, 53)
( 39, 55)( 40, 48)( 41, 50)( 42, 49)( 43, 51)( 65, 66)( 68, 80)( 69, 82)
( 70, 81)( 71, 83)( 72, 76)( 73, 78)( 74, 77)( 75, 79)( 84,104)( 85,106)
( 86,105)( 87,107)( 88,120)( 89,122)( 90,121)( 91,123)( 92,116)( 93,118)
( 94,117)( 95,119)( 96,112)( 97,114)( 98,113)( 99,115)(100,108)(101,110)
(102,109)(103,111);;
s4 := ( 4, 88)( 5, 89)( 6, 91)( 7, 90)( 8, 84)( 9, 85)( 10, 87)( 11, 86)
( 12,100)( 13,101)( 14,103)( 15,102)( 16, 96)( 17, 97)( 18, 99)( 19, 98)
( 20, 92)( 21, 93)( 22, 95)( 23, 94)( 24, 68)( 25, 69)( 26, 71)( 27, 70)
( 28, 64)( 29, 65)( 30, 67)( 31, 66)( 32, 80)( 33, 81)( 34, 83)( 35, 82)
( 36, 76)( 37, 77)( 38, 79)( 39, 78)( 40, 72)( 41, 73)( 42, 75)( 43, 74)
( 44,108)( 45,109)( 46,111)( 47,110)( 48,104)( 49,105)( 50,107)( 51,106)
( 52,120)( 53,121)( 54,123)( 55,122)( 56,116)( 57,117)( 58,119)( 59,118)
( 60,112)( 61,113)( 62,115)( 63,114);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, 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*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s4*s3*s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(123)!(2,3);
s1 := Sym(123)!(1,2);
s2 := Sym(123)!( 4, 65)( 5, 64)( 6, 67)( 7, 66)( 8, 69)( 9, 68)( 10, 71)
( 11, 70)( 12, 73)( 13, 72)( 14, 75)( 15, 74)( 16, 77)( 17, 76)( 18, 79)
( 19, 78)( 20, 81)( 21, 80)( 22, 83)( 23, 82)( 24, 85)( 25, 84)( 26, 87)
( 27, 86)( 28, 89)( 29, 88)( 30, 91)( 31, 90)( 32, 93)( 33, 92)( 34, 95)
( 35, 94)( 36, 97)( 37, 96)( 38, 99)( 39, 98)( 40,101)( 41,100)( 42,103)
( 43,102)( 44,105)( 45,104)( 46,107)( 47,106)( 48,109)( 49,108)( 50,111)
( 51,110)( 52,113)( 53,112)( 54,115)( 55,114)( 56,117)( 57,116)( 58,119)
( 59,118)( 60,121)( 61,120)( 62,123)( 63,122);
s3 := Sym(123)!( 5, 6)( 8, 20)( 9, 22)( 10, 21)( 11, 23)( 12, 16)( 13, 18)
( 14, 17)( 15, 19)( 24, 44)( 25, 46)( 26, 45)( 27, 47)( 28, 60)( 29, 62)
( 30, 61)( 31, 63)( 32, 56)( 33, 58)( 34, 57)( 35, 59)( 36, 52)( 37, 54)
( 38, 53)( 39, 55)( 40, 48)( 41, 50)( 42, 49)( 43, 51)( 65, 66)( 68, 80)
( 69, 82)( 70, 81)( 71, 83)( 72, 76)( 73, 78)( 74, 77)( 75, 79)( 84,104)
( 85,106)( 86,105)( 87,107)( 88,120)( 89,122)( 90,121)( 91,123)( 92,116)
( 93,118)( 94,117)( 95,119)( 96,112)( 97,114)( 98,113)( 99,115)(100,108)
(101,110)(102,109)(103,111);
s4 := Sym(123)!( 4, 88)( 5, 89)( 6, 91)( 7, 90)( 8, 84)( 9, 85)( 10, 87)
( 11, 86)( 12,100)( 13,101)( 14,103)( 15,102)( 16, 96)( 17, 97)( 18, 99)
( 19, 98)( 20, 92)( 21, 93)( 22, 95)( 23, 94)( 24, 68)( 25, 69)( 26, 71)
( 27, 70)( 28, 64)( 29, 65)( 30, 67)( 31, 66)( 32, 80)( 33, 81)( 34, 83)
( 35, 82)( 36, 76)( 37, 77)( 38, 79)( 39, 78)( 40, 72)( 41, 73)( 42, 75)
( 43, 74)( 44,108)( 45,109)( 46,111)( 47,110)( 48,104)( 49,105)( 50,107)
( 51,106)( 52,120)( 53,121)( 54,123)( 55,122)( 56,116)( 57,117)( 58,119)
( 59,118)( 60,112)( 61,113)( 62,115)( 63,114);
poly := sub<Sym(123)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, 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*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s4*s3*s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s2 >;
to this polytope