Polytope of Type {2,2,2,15,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,2,15,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240411)
Rank : 6
Schlafli Type : {2,2,2,15,4}
Number of vertices, edges, etc : 2, 2, 2, 30, 60, 8
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 : {2,2,2,15,4}*960
4-fold quotients : {2,2,2,15,2}*480
5-fold quotients : {2,2,2,3,4}*384
10-fold quotients : {2,2,2,3,4}*192
12-fold quotients : {2,2,2,5,2}*160
20-fold quotients : {2,2,2,3,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (5,6);;
s3 := ( 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);;
s4 := ( 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);;
s5 := ( 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)
( 63,126)( 64,125)( 65,124)( 66,123);;
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, s4*s5*s4*s5*s4*s5*s4*s5,
s3*s4*s5*s4*s3*s4*s3*s4*s5*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*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(126)!(1,2);
s1 := Sym(126)!(3,4);
s2 := Sym(126)!(5,6);
s3 := 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);
s4 := 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);
s5 := Sym(126)!( 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)( 63,126)( 64,125)( 65,124)( 66,123);
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, s4*s5*s4*s5*s4*s5*s4*s5,
s3*s4*s5*s4*s3*s4*s3*s4*s5*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*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope