Polytope of Type {2,2,2,4,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,4,15}*1920
if this polytope has a name.
Group : SmallGroup(1920,240411)
Rank : 6
Schlafli Type : {2,2,2,4,15}
Number of vertices, edges, etc : 2, 2, 2, 8, 60, 30
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 : {2,2,2,4,15}*960
4-fold quotients : {2,2,2,2,15}*480
5-fold quotients : {2,2,2,4,3}*384
10-fold quotients : {2,2,2,4,3}*192
12-fold quotients : {2,2,2,2,5}*160
20-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 := (5,6);;
s3 := ( 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)
( 63,124)( 64,123)( 65,126)( 66,125);;
s4 := ( 8, 9)( 11, 23)( 12, 25)( 13, 24)( 14, 26)( 15, 19)( 16, 21)( 17, 20)
( 18, 22)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 63)( 32, 65)( 33, 64)
( 34, 66)( 35, 59)( 36, 61)( 37, 60)( 38, 62)( 39, 55)( 40, 57)( 41, 56)
( 42, 58)( 43, 51)( 44, 53)( 45, 52)( 46, 54)( 68, 69)( 71, 83)( 72, 85)
( 73, 84)( 74, 86)( 75, 79)( 76, 81)( 77, 80)( 78, 82)( 87,107)( 88,109)
( 89,108)( 90,110)( 91,123)( 92,125)( 93,124)( 94,126)( 95,119)( 96,121)
( 97,120)( 98,122)( 99,115)(100,117)(101,116)(102,118)(103,111)(104,113)
(105,112)(106,114);;
s5 := ( 7, 31)( 8, 32)( 9, 34)( 10, 33)( 11, 27)( 12, 28)( 13, 30)( 14, 29)
( 15, 43)( 16, 44)( 17, 46)( 18, 45)( 19, 39)( 20, 40)( 21, 42)( 22, 41)
( 23, 35)( 24, 36)( 25, 38)( 26, 37)( 47, 51)( 48, 52)( 49, 54)( 50, 53)
( 55, 63)( 56, 64)( 57, 66)( 58, 65)( 61, 62)( 67, 91)( 68, 92)( 69, 94)
( 70, 93)( 71, 87)( 72, 88)( 73, 90)( 74, 89)( 75,103)( 76,104)( 77,106)
( 78,105)( 79, 99)( 80,100)( 81,102)( 82,101)( 83, 95)( 84, 96)( 85, 98)
( 86, 97)(107,111)(108,112)(109,114)(110,113)(115,123)(116,124)(117,126)
(118,125)(121,122);;
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, s2*s3*s2*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, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s5*s4*s5*s4*s3*s4*s5*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(126)!(1,2);
s1 := Sym(126)!(3,4);
s2 := Sym(126)!(5,6);
s3 := Sym(126)!( 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)( 63,124)( 64,123)( 65,126)( 66,125);
s4 := Sym(126)!( 8, 9)( 11, 23)( 12, 25)( 13, 24)( 14, 26)( 15, 19)( 16, 21)
( 17, 20)( 18, 22)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 63)( 32, 65)
( 33, 64)( 34, 66)( 35, 59)( 36, 61)( 37, 60)( 38, 62)( 39, 55)( 40, 57)
( 41, 56)( 42, 58)( 43, 51)( 44, 53)( 45, 52)( 46, 54)( 68, 69)( 71, 83)
( 72, 85)( 73, 84)( 74, 86)( 75, 79)( 76, 81)( 77, 80)( 78, 82)( 87,107)
( 88,109)( 89,108)( 90,110)( 91,123)( 92,125)( 93,124)( 94,126)( 95,119)
( 96,121)( 97,120)( 98,122)( 99,115)(100,117)(101,116)(102,118)(103,111)
(104,113)(105,112)(106,114);
s5 := Sym(126)!( 7, 31)( 8, 32)( 9, 34)( 10, 33)( 11, 27)( 12, 28)( 13, 30)
( 14, 29)( 15, 43)( 16, 44)( 17, 46)( 18, 45)( 19, 39)( 20, 40)( 21, 42)
( 22, 41)( 23, 35)( 24, 36)( 25, 38)( 26, 37)( 47, 51)( 48, 52)( 49, 54)
( 50, 53)( 55, 63)( 56, 64)( 57, 66)( 58, 65)( 61, 62)( 67, 91)( 68, 92)
( 69, 94)( 70, 93)( 71, 87)( 72, 88)( 73, 90)( 74, 89)( 75,103)( 76,104)
( 77,106)( 78,105)( 79, 99)( 80,100)( 81,102)( 82,101)( 83, 95)( 84, 96)
( 85, 98)( 86, 97)(107,111)(108,112)(109,114)(110,113)(115,123)(116,124)
(117,126)(118,125)(121,122);
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,
s1*s2*s1*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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s5*s4*s5*s4*s3*s4*s5*s4*s5*s4,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;
to this polytope