Polytope of Type {120,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,2}*480
if this polytope has a name.
Group : SmallGroup(480,868)
Rank : 3
Schlafli Type : {120,2}
Number of vertices, edges, etc : 120, 120, 2
Order of s0s1s2 : 120
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{120,2,2} of size 960
{120,2,3} of size 1440
{120,2,4} of size 1920
Vertex Figure Of :
{2,120,2} of size 960
{4,120,2} of size 1920
{4,120,2} of size 1920
{4,120,2} of size 1920
{4,120,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {60,2}*240
3-fold quotients : {40,2}*160
4-fold quotients : {30,2}*120
5-fold quotients : {24,2}*96
6-fold quotients : {20,2}*80
8-fold quotients : {15,2}*60
10-fold quotients : {12,2}*48
12-fold quotients : {10,2}*40
15-fold quotients : {8,2}*32
20-fold quotients : {6,2}*24
24-fold quotients : {5,2}*20
30-fold quotients : {4,2}*16
40-fold quotients : {3,2}*12
60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {120,4}*960a, {240,2}*960
3-fold covers : {360,2}*1440, {120,6}*1440b, {120,6}*1440c
4-fold covers : {120,4}*1920a, {120,8}*1920b, {120,8}*1920c, {240,4}*1920a, {240,4}*1920b, {480,2}*1920, {120,4}*1920c
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)( 17, 20)
( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 46)( 32, 50)
( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)( 40, 57)
( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 61, 91)( 62, 95)( 63, 94)
( 64, 93)( 65, 92)( 66,101)( 67,105)( 68,104)( 69,103)( 70,102)( 71, 96)
( 72,100)( 73, 99)( 74, 98)( 75, 97)( 76,106)( 77,110)( 78,109)( 79,108)
( 80,107)( 81,116)( 82,120)( 83,119)( 84,118)( 85,117)( 86,111)( 87,115)
( 88,114)( 89,113)( 90,112);;
s1 := ( 1, 67)( 2, 66)( 3, 70)( 4, 69)( 5, 68)( 6, 62)( 7, 61)( 8, 65)
( 9, 64)( 10, 63)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)( 16, 82)
( 17, 81)( 18, 85)( 19, 84)( 20, 83)( 21, 77)( 22, 76)( 23, 80)( 24, 79)
( 25, 78)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31,112)( 32,111)
( 33,115)( 34,114)( 35,113)( 36,107)( 37,106)( 38,110)( 39,109)( 40,108)
( 41,117)( 42,116)( 43,120)( 44,119)( 45,118)( 46, 97)( 47, 96)( 48,100)
( 49, 99)( 50, 98)( 51, 92)( 52, 91)( 53, 95)( 54, 94)( 55, 93)( 56,102)
( 57,101)( 58,105)( 59,104)( 60,103);;
s2 := (121,122);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(122)!( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)
( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 31, 46)
( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 56)( 37, 60)( 38, 59)( 39, 58)
( 40, 57)( 41, 51)( 42, 55)( 43, 54)( 44, 53)( 45, 52)( 61, 91)( 62, 95)
( 63, 94)( 64, 93)( 65, 92)( 66,101)( 67,105)( 68,104)( 69,103)( 70,102)
( 71, 96)( 72,100)( 73, 99)( 74, 98)( 75, 97)( 76,106)( 77,110)( 78,109)
( 79,108)( 80,107)( 81,116)( 82,120)( 83,119)( 84,118)( 85,117)( 86,111)
( 87,115)( 88,114)( 89,113)( 90,112);
s1 := Sym(122)!( 1, 67)( 2, 66)( 3, 70)( 4, 69)( 5, 68)( 6, 62)( 7, 61)
( 8, 65)( 9, 64)( 10, 63)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)
( 16, 82)( 17, 81)( 18, 85)( 19, 84)( 20, 83)( 21, 77)( 22, 76)( 23, 80)
( 24, 79)( 25, 78)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31,112)
( 32,111)( 33,115)( 34,114)( 35,113)( 36,107)( 37,106)( 38,110)( 39,109)
( 40,108)( 41,117)( 42,116)( 43,120)( 44,119)( 45,118)( 46, 97)( 47, 96)
( 48,100)( 49, 99)( 50, 98)( 51, 92)( 52, 91)( 53, 95)( 54, 94)( 55, 93)
( 56,102)( 57,101)( 58,105)( 59,104)( 60,103);
s2 := Sym(122)!(121,122);
poly := sub<Sym(122)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope