Polytope of Type {4,2,15,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,15,4}*1920
if this polytope has a name.
Group : SmallGroup(1920,240291)
Rank : 5
Schlafli Type : {4,2,15,4}
Number of vertices, edges, etc : 4, 4, 30, 60, 8
Order of s0s1s2s3s4 : 60
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 : {4,2,15,4}*960, {2,2,15,4}*960
4-fold quotients : {4,2,15,2}*480, {2,2,15,4}*480
5-fold quotients : {4,2,3,4}*384
8-fold quotients : {2,2,15,2}*240
10-fold quotients : {4,2,3,4}*192, {2,2,3,4}*192
12-fold quotients : {4,2,5,2}*160
20-fold quotients : {4,2,3,2}*96, {2,2,3,4}*96
24-fold quotients : {2,2,5,2}*80
40-fold quotients : {2,2,3,2}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 9, 21)( 10, 23)( 11, 22)( 12, 24)( 13, 17)( 14, 19)( 15, 18)
( 16, 20)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 61)( 30, 63)( 31, 62)
( 32, 64)( 33, 57)( 34, 59)( 35, 58)( 36, 60)( 37, 53)( 38, 55)( 39, 54)
( 40, 56)( 41, 49)( 42, 51)( 43, 50)( 44, 52)( 66, 67)( 69, 81)( 70, 83)
( 71, 82)( 72, 84)( 73, 77)( 74, 79)( 75, 78)( 76, 80)( 85,105)( 86,107)
( 87,106)( 88,108)( 89,121)( 90,123)( 91,122)( 92,124)( 93,117)( 94,119)
( 95,118)( 96,120)( 97,113)( 98,115)( 99,114)(100,116)(101,109)(102,111)
(103,110)(104,112);;
s3 := ( 5, 29)( 6, 30)( 7, 32)( 8, 31)( 9, 25)( 10, 26)( 11, 28)( 12, 27)
( 13, 41)( 14, 42)( 15, 44)( 16, 43)( 17, 37)( 18, 38)( 19, 40)( 20, 39)
( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 45, 49)( 46, 50)( 47, 52)( 48, 51)
( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 59, 60)( 65, 89)( 66, 90)( 67, 92)
( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73,101)( 74,102)( 75,104)
( 76,103)( 77, 97)( 78, 98)( 79,100)( 80, 99)( 81, 93)( 82, 94)( 83, 96)
( 84, 95)(105,109)(106,110)(107,112)(108,111)(113,121)(114,122)(115,124)
(116,123)(119,120);;
s4 := ( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 72)( 10, 71)( 11, 70)( 12, 69)
( 13, 76)( 14, 75)( 15, 74)( 16, 73)( 17, 80)( 18, 79)( 19, 78)( 20, 77)
( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 88)( 26, 87)( 27, 86)( 28, 85)
( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 96)( 34, 95)( 35, 94)( 36, 93)
( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41,104)( 42,103)( 43,102)( 44,101)
( 45,108)( 46,107)( 47,106)( 48,105)( 49,112)( 50,111)( 51,110)( 52,109)
( 53,116)( 54,115)( 55,114)( 56,113)( 57,120)( 58,119)( 59,118)( 60,117)
( 61,124)( 62,123)( 63,122)( 64,121);;
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*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(124)!(2,3);
s1 := Sym(124)!(1,2)(3,4);
s2 := Sym(124)!( 6, 7)( 9, 21)( 10, 23)( 11, 22)( 12, 24)( 13, 17)( 14, 19)
( 15, 18)( 16, 20)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 61)( 30, 63)
( 31, 62)( 32, 64)( 33, 57)( 34, 59)( 35, 58)( 36, 60)( 37, 53)( 38, 55)
( 39, 54)( 40, 56)( 41, 49)( 42, 51)( 43, 50)( 44, 52)( 66, 67)( 69, 81)
( 70, 83)( 71, 82)( 72, 84)( 73, 77)( 74, 79)( 75, 78)( 76, 80)( 85,105)
( 86,107)( 87,106)( 88,108)( 89,121)( 90,123)( 91,122)( 92,124)( 93,117)
( 94,119)( 95,118)( 96,120)( 97,113)( 98,115)( 99,114)(100,116)(101,109)
(102,111)(103,110)(104,112);
s3 := Sym(124)!( 5, 29)( 6, 30)( 7, 32)( 8, 31)( 9, 25)( 10, 26)( 11, 28)
( 12, 27)( 13, 41)( 14, 42)( 15, 44)( 16, 43)( 17, 37)( 18, 38)( 19, 40)
( 20, 39)( 21, 33)( 22, 34)( 23, 36)( 24, 35)( 45, 49)( 46, 50)( 47, 52)
( 48, 51)( 53, 61)( 54, 62)( 55, 64)( 56, 63)( 59, 60)( 65, 89)( 66, 90)
( 67, 92)( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73,101)( 74,102)
( 75,104)( 76,103)( 77, 97)( 78, 98)( 79,100)( 80, 99)( 81, 93)( 82, 94)
( 83, 96)( 84, 95)(105,109)(106,110)(107,112)(108,111)(113,121)(114,122)
(115,124)(116,123)(119,120);
s4 := Sym(124)!( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 72)( 10, 71)( 11, 70)
( 12, 69)( 13, 76)( 14, 75)( 15, 74)( 16, 73)( 17, 80)( 18, 79)( 19, 78)
( 20, 77)( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 88)( 26, 87)( 27, 86)
( 28, 85)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 96)( 34, 95)( 35, 94)
( 36, 93)( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41,104)( 42,103)( 43,102)
( 44,101)( 45,108)( 46,107)( 47,106)( 48,105)( 49,112)( 50,111)( 51,110)
( 52,109)( 53,116)( 54,115)( 55,114)( 56,113)( 57,120)( 58,119)( 59,118)
( 60,117)( 61,124)( 62,123)( 63,122)( 64,121);
poly := sub<Sym(124)|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*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