Polytope of Type {3,2,15,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,15,4}*1440
if this polytope has a name.
Group : SmallGroup(1440,5900)
Rank : 5
Schlafli Type : {3,2,15,4}
Number of vertices, edges, etc : 3, 3, 30, 60, 8
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 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 : {3,2,15,4}*720
4-fold quotients : {3,2,15,2}*360
5-fold quotients : {3,2,3,4}*288
10-fold quotients : {3,2,3,4}*144
12-fold quotients : {3,2,5,2}*120
20-fold quotients : {3,2,3,2}*72
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 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);;
s3 := ( 4, 28)( 5, 29)( 6, 31)( 7, 30)( 8, 24)( 9, 25)( 10, 27)( 11, 26)
( 12, 40)( 13, 41)( 14, 43)( 15, 42)( 16, 36)( 17, 37)( 18, 39)( 19, 38)
( 20, 32)( 21, 33)( 22, 35)( 23, 34)( 44, 48)( 45, 49)( 46, 51)( 47, 50)
( 52, 60)( 53, 61)( 54, 63)( 55, 62)( 58, 59)( 64, 88)( 65, 89)( 66, 91)
( 67, 90)( 68, 84)( 69, 85)( 70, 87)( 71, 86)( 72,100)( 73,101)( 74,103)
( 75,102)( 76, 96)( 77, 97)( 78, 99)( 79, 98)( 80, 92)( 81, 93)( 82, 95)
( 83, 94)(104,108)(105,109)(106,111)(107,110)(112,120)(113,121)(114,123)
(115,122)(118,119);;
s4 := ( 4, 67)( 5, 66)( 6, 65)( 7, 64)( 8, 71)( 9, 70)( 10, 69)( 11, 68)
( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 79)( 17, 78)( 18, 77)( 19, 76)
( 20, 83)( 21, 82)( 22, 81)( 23, 80)( 24, 87)( 25, 86)( 26, 85)( 27, 84)
( 28, 91)( 29, 90)( 30, 89)( 31, 88)( 32, 95)( 33, 94)( 34, 93)( 35, 92)
( 36, 99)( 37, 98)( 38, 97)( 39, 96)( 40,103)( 41,102)( 42,101)( 43,100)
( 44,107)( 45,106)( 46,105)( 47,104)( 48,111)( 49,110)( 50,109)( 51,108)
( 52,115)( 53,114)( 54,113)( 55,112)( 56,119)( 57,118)( 58,117)( 59,116)
( 60,123)( 61,122)( 62,121)( 63,120);;
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, s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s3*s2*s3*s2*s3*s4*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*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(123)!(2,3);
s1 := Sym(123)!(1,2);
s2 := 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);
s3 := Sym(123)!( 4, 28)( 5, 29)( 6, 31)( 7, 30)( 8, 24)( 9, 25)( 10, 27)
( 11, 26)( 12, 40)( 13, 41)( 14, 43)( 15, 42)( 16, 36)( 17, 37)( 18, 39)
( 19, 38)( 20, 32)( 21, 33)( 22, 35)( 23, 34)( 44, 48)( 45, 49)( 46, 51)
( 47, 50)( 52, 60)( 53, 61)( 54, 63)( 55, 62)( 58, 59)( 64, 88)( 65, 89)
( 66, 91)( 67, 90)( 68, 84)( 69, 85)( 70, 87)( 71, 86)( 72,100)( 73,101)
( 74,103)( 75,102)( 76, 96)( 77, 97)( 78, 99)( 79, 98)( 80, 92)( 81, 93)
( 82, 95)( 83, 94)(104,108)(105,109)(106,111)(107,110)(112,120)(113,121)
(114,123)(115,122)(118,119);
s4 := Sym(123)!( 4, 67)( 5, 66)( 6, 65)( 7, 64)( 8, 71)( 9, 70)( 10, 69)
( 11, 68)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 79)( 17, 78)( 18, 77)
( 19, 76)( 20, 83)( 21, 82)( 22, 81)( 23, 80)( 24, 87)( 25, 86)( 26, 85)
( 27, 84)( 28, 91)( 29, 90)( 30, 89)( 31, 88)( 32, 95)( 33, 94)( 34, 93)
( 35, 92)( 36, 99)( 37, 98)( 38, 97)( 39, 96)( 40,103)( 41,102)( 42,101)
( 43,100)( 44,107)( 45,106)( 46,105)( 47,104)( 48,111)( 49,110)( 50,109)
( 51,108)( 52,115)( 53,114)( 54,113)( 55,112)( 56,119)( 57,118)( 58,117)
( 59,116)( 60,123)( 61,122)( 62,121)( 63,120);
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,
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s3*s2*s3*s2*s3*s4*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*s2*s3*s2*s3 >;
to this polytope