Polytope of Type {2,120}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,120}*480
if this polytope has a name.
Group : SmallGroup(480,868)
Rank : 3
Schlafli Type : {2,120}
Number of vertices, edges, etc : 2, 120, 120
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,120,2} of size 960
   {2,120,4} of size 1920
   {2,120,4} of size 1920
   {2,120,4} of size 1920
   {2,120,4} of size 1920
Vertex Figure Of :
   {2,2,120} of size 960
   {3,2,120} of size 1440
   {4,2,120} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,60}*240
   3-fold quotients : {2,40}*160
   4-fold quotients : {2,30}*120
   5-fold quotients : {2,24}*96
   6-fold quotients : {2,20}*80
   8-fold quotients : {2,15}*60
   10-fold quotients : {2,12}*48
   12-fold quotients : {2,10}*40
   15-fold quotients : {2,8}*32
   20-fold quotients : {2,6}*24
   24-fold quotients : {2,5}*20
   30-fold quotients : {2,4}*16
   40-fold quotients : {2,3}*12
   60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,120}*960a, {2,240}*960
   3-fold covers : {2,360}*1440, {6,120}*1440b, {6,120}*1440c
   4-fold covers : {4,120}*1920a, {8,120}*1920b, {8,120}*1920c, {4,240}*1920a, {4,240}*1920b, {2,480}*1920, {4,120}*1920c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 19, 22)
( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 33, 48)( 34, 52)
( 35, 51)( 36, 50)( 37, 49)( 38, 58)( 39, 62)( 40, 61)( 41, 60)( 42, 59)
( 43, 53)( 44, 57)( 45, 56)( 46, 55)( 47, 54)( 63, 93)( 64, 97)( 65, 96)
( 66, 95)( 67, 94)( 68,103)( 69,107)( 70,106)( 71,105)( 72,104)( 73, 98)
( 74,102)( 75,101)( 76,100)( 77, 99)( 78,108)( 79,112)( 80,111)( 81,110)
( 82,109)( 83,118)( 84,122)( 85,121)( 86,120)( 87,119)( 88,113)( 89,117)
( 90,116)( 91,115)( 92,114);;
s2 := (  3, 69)(  4, 68)(  5, 72)(  6, 71)(  7, 70)(  8, 64)(  9, 63)( 10, 67)
( 11, 66)( 12, 65)( 13, 74)( 14, 73)( 15, 77)( 16, 76)( 17, 75)( 18, 84)
( 19, 83)( 20, 87)( 21, 86)( 22, 85)( 23, 79)( 24, 78)( 25, 82)( 26, 81)
( 27, 80)( 28, 89)( 29, 88)( 30, 92)( 31, 91)( 32, 90)( 33,114)( 34,113)
( 35,117)( 36,116)( 37,115)( 38,109)( 39,108)( 40,112)( 41,111)( 42,110)
( 43,119)( 44,118)( 45,122)( 46,121)( 47,120)( 48, 99)( 49, 98)( 50,102)
( 51,101)( 52,100)( 53, 94)( 54, 93)( 55, 97)( 56, 96)( 57, 95)( 58,104)
( 59,103)( 60,107)( 61,106)( 62,105);;
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*s1*s0*s1, s0*s2*s0*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*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*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(122)!(1,2);
s1 := Sym(122)!(  4,  7)(  5,  6)(  8, 13)(  9, 17)( 10, 16)( 11, 15)( 12, 14)
( 19, 22)( 20, 21)( 23, 28)( 24, 32)( 25, 31)( 26, 30)( 27, 29)( 33, 48)
( 34, 52)( 35, 51)( 36, 50)( 37, 49)( 38, 58)( 39, 62)( 40, 61)( 41, 60)
( 42, 59)( 43, 53)( 44, 57)( 45, 56)( 46, 55)( 47, 54)( 63, 93)( 64, 97)
( 65, 96)( 66, 95)( 67, 94)( 68,103)( 69,107)( 70,106)( 71,105)( 72,104)
( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99)( 78,108)( 79,112)( 80,111)
( 81,110)( 82,109)( 83,118)( 84,122)( 85,121)( 86,120)( 87,119)( 88,113)
( 89,117)( 90,116)( 91,115)( 92,114);
s2 := Sym(122)!(  3, 69)(  4, 68)(  5, 72)(  6, 71)(  7, 70)(  8, 64)(  9, 63)
( 10, 67)( 11, 66)( 12, 65)( 13, 74)( 14, 73)( 15, 77)( 16, 76)( 17, 75)
( 18, 84)( 19, 83)( 20, 87)( 21, 86)( 22, 85)( 23, 79)( 24, 78)( 25, 82)
( 26, 81)( 27, 80)( 28, 89)( 29, 88)( 30, 92)( 31, 91)( 32, 90)( 33,114)
( 34,113)( 35,117)( 36,116)( 37,115)( 38,109)( 39,108)( 40,112)( 41,111)
( 42,110)( 43,119)( 44,118)( 45,122)( 46,121)( 47,120)( 48, 99)( 49, 98)
( 50,102)( 51,101)( 52,100)( 53, 94)( 54, 93)( 55, 97)( 56, 96)( 57, 95)
( 58,104)( 59,103)( 60,107)( 61,106)( 62,105);
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*s1*s0*s1, s0*s2*s0*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*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*s1*s2 >;

to this polytope