Polytope of Type {2,4,15,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,15,2,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,240411)
Rank : 6
Schlafli Type : {2,4,15,2,2}
Number of vertices, edges, etc : 2, 8, 60, 30, 2, 2
Order of s0s1s2s3s4s5 : 30
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 : {2,4,15,2,2}*960
4-fold quotients : {2,2,15,2,2}*480
5-fold quotients : {2,4,3,2,2}*384
10-fold quotients : {2,4,3,2,2}*192
12-fold quotients : {2,2,5,2,2}*160
20-fold quotients : {2,2,3,2,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 64)( 4, 63)( 5, 66)( 6, 65)( 7, 68)( 8, 67)( 9, 70)( 10, 69)
( 11, 72)( 12, 71)( 13, 74)( 14, 73)( 15, 76)( 16, 75)( 17, 78)( 18, 77)
( 19, 80)( 20, 79)( 21, 82)( 22, 81)( 23, 84)( 24, 83)( 25, 86)( 26, 85)
( 27, 88)( 28, 87)( 29, 90)( 30, 89)( 31, 92)( 32, 91)( 33, 94)( 34, 93)
( 35, 96)( 36, 95)( 37, 98)( 38, 97)( 39,100)( 40, 99)( 41,102)( 42,101)
( 43,104)( 44,103)( 45,106)( 46,105)( 47,108)( 48,107)( 49,110)( 50,109)
( 51,112)( 52,111)( 53,114)( 54,113)( 55,116)( 56,115)( 57,118)( 58,117)
( 59,120)( 60,119)( 61,122)( 62,121);;
s2 := ( 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);;
s3 := ( 3, 27)( 4, 28)( 5, 30)( 6, 29)( 7, 23)( 8, 24)( 9, 26)( 10, 25)
( 11, 39)( 12, 40)( 13, 42)( 14, 41)( 15, 35)( 16, 36)( 17, 38)( 18, 37)
( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 43, 47)( 44, 48)( 45, 50)( 46, 49)
( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 57, 58)( 63, 87)( 64, 88)( 65, 90)
( 66, 89)( 67, 83)( 68, 84)( 69, 86)( 70, 85)( 71, 99)( 72,100)( 73,102)
( 74,101)( 75, 95)( 76, 96)( 77, 98)( 78, 97)( 79, 91)( 80, 92)( 81, 94)
( 82, 93)(103,107)(104,108)(105,110)(106,109)(111,119)(112,120)(113,122)
(114,121)(117,118);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(126)!(1,2);
s1 := Sym(126)!( 3, 64)( 4, 63)( 5, 66)( 6, 65)( 7, 68)( 8, 67)( 9, 70)
( 10, 69)( 11, 72)( 12, 71)( 13, 74)( 14, 73)( 15, 76)( 16, 75)( 17, 78)
( 18, 77)( 19, 80)( 20, 79)( 21, 82)( 22, 81)( 23, 84)( 24, 83)( 25, 86)
( 26, 85)( 27, 88)( 28, 87)( 29, 90)( 30, 89)( 31, 92)( 32, 91)( 33, 94)
( 34, 93)( 35, 96)( 36, 95)( 37, 98)( 38, 97)( 39,100)( 40, 99)( 41,102)
( 42,101)( 43,104)( 44,103)( 45,106)( 46,105)( 47,108)( 48,107)( 49,110)
( 50,109)( 51,112)( 52,111)( 53,114)( 54,113)( 55,116)( 56,115)( 57,118)
( 58,117)( 59,120)( 60,119)( 61,122)( 62,121);
s2 := 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);
s3 := Sym(126)!( 3, 27)( 4, 28)( 5, 30)( 6, 29)( 7, 23)( 8, 24)( 9, 26)
( 10, 25)( 11, 39)( 12, 40)( 13, 42)( 14, 41)( 15, 35)( 16, 36)( 17, 38)
( 18, 37)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 43, 47)( 44, 48)( 45, 50)
( 46, 49)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 57, 58)( 63, 87)( 64, 88)
( 65, 90)( 66, 89)( 67, 83)( 68, 84)( 69, 86)( 70, 85)( 71, 99)( 72,100)
( 73,102)( 74,101)( 75, 95)( 76, 96)( 77, 98)( 78, 97)( 79, 91)( 80, 92)
( 81, 94)( 82, 93)(103,107)(104,108)(105,110)(106,109)(111,119)(112,120)
(113,122)(114,121)(117,118);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope