Polytope of Type {4,60,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,60,2,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,205027)
Rank : 5
Schlafli Type : {4,60,2,2}
Number of vertices, edges, etc : 4, 120, 60, 2, 2
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 : {2,60,2,2}*960, {4,30,2,2}*960a
3-fold quotients : {4,20,2,2}*640
4-fold quotients : {2,30,2,2}*480
5-fold quotients : {4,12,2,2}*384a
6-fold quotients : {2,20,2,2}*320, {4,10,2,2}*320
8-fold quotients : {2,15,2,2}*240
10-fold quotients : {2,12,2,2}*192, {4,6,2,2}*192a
12-fold quotients : {2,10,2,2}*160
15-fold quotients : {4,4,2,2}*128
20-fold quotients : {2,6,2,2}*96
24-fold quotients : {2,5,2,2}*80
30-fold quotients : {2,4,2,2}*64, {4,2,2,2}*64
40-fold quotients : {2,3,2,2}*48
60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)
( 69, 84)( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 91,106)
( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)
(100,115)(101,116)(102,117)(103,118)(104,119)(105,120);;
s1 := ( 1, 61)( 2, 65)( 3, 64)( 4, 63)( 5, 62)( 6, 71)( 7, 75)( 8, 74)
( 9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)( 16, 76)
( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 86)( 22, 90)( 23, 89)( 24, 88)
( 25, 87)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 91)( 32, 95)
( 33, 94)( 34, 93)( 35, 92)( 36,101)( 37,105)( 38,104)( 39,103)( 40,102)
( 41, 96)( 42,100)( 43, 99)( 44, 98)( 45, 97)( 46,106)( 47,110)( 48,109)
( 49,108)( 50,107)( 51,116)( 52,120)( 53,119)( 54,118)( 55,117)( 56,111)
( 57,115)( 58,114)( 59,113)( 60,112);;
s2 := ( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)( 48, 55)
( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 97)( 62, 96)( 63,100)( 64, 99)
( 65, 98)( 66, 92)( 67, 91)( 68, 95)( 69, 94)( 70, 93)( 71,102)( 72,101)
( 73,105)( 74,104)( 75,103)( 76,112)( 77,111)( 78,115)( 79,114)( 80,113)
( 81,107)( 82,106)( 83,110)( 84,109)( 85,108)( 86,117)( 87,116)( 88,120)
( 89,119)( 90,118);;
s3 := (121,122);;
s4 := (123,124);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(124)!( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)
( 68, 83)( 69, 84)( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)
( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)
( 99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120);
s1 := Sym(124)!( 1, 61)( 2, 65)( 3, 64)( 4, 63)( 5, 62)( 6, 71)( 7, 75)
( 8, 74)( 9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)
( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 86)( 22, 90)( 23, 89)
( 24, 88)( 25, 87)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 91)
( 32, 95)( 33, 94)( 34, 93)( 35, 92)( 36,101)( 37,105)( 38,104)( 39,103)
( 40,102)( 41, 96)( 42,100)( 43, 99)( 44, 98)( 45, 97)( 46,106)( 47,110)
( 48,109)( 49,108)( 50,107)( 51,116)( 52,120)( 53,119)( 54,118)( 55,117)
( 56,111)( 57,115)( 58,114)( 59,113)( 60,112);
s2 := Sym(124)!( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)
( 32, 36)( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 97)( 62, 96)( 63,100)
( 64, 99)( 65, 98)( 66, 92)( 67, 91)( 68, 95)( 69, 94)( 70, 93)( 71,102)
( 72,101)( 73,105)( 74,104)( 75,103)( 76,112)( 77,111)( 78,115)( 79,114)
( 80,113)( 81,107)( 82,106)( 83,110)( 84,109)( 85,108)( 86,117)( 87,116)
( 88,120)( 89,119)( 90,118);
s3 := Sym(124)!(121,122);
s4 := Sym(124)!(123,124);
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, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope