Polytope of Type {2,240}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,240}*960
if this polytope has a name.
Group : SmallGroup(960,5198)
Rank : 3
Schlafli Type : {2,240}
Number of vertices, edges, etc : 2, 240, 240
Order of s₀s₁s₂ : 240
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,240,2} of size 1920
Vertex Figure Of :
   {2,2,240} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,120}*480
   3-fold quotients : {2,80}*320
   4-fold quotients : {2,60}*240
   5-fold quotients : {2,48}*192
   6-fold quotients : {2,40}*160
   8-fold quotients : {2,30}*120
   10-fold quotients : {2,24}*96
   12-fold quotients : {2,20}*80
   15-fold quotients : {2,16}*64
   16-fold quotients : {2,15}*60
   20-fold quotients : {2,12}*48
   24-fold quotients : {2,10}*40
   30-fold quotients : {2,8}*32
   40-fold quotients : {2,6}*24
   48-fold quotients : {2,5}*20
   60-fold quotients : {2,4}*16
   80-fold quotients : {2,3}*12
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,240}*1920a, {2,480}*1920

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)(123,183)(124,187)(125,186)(126,185)(127,184)(128,193)(129,197)(130,196)(131,195)(132,194)(133,188)(134,192)(135,191)(136,190)(137,189)(138,198)(139,202)(140,201)(141,200)(142,199)(143,208)(144,212)(145,211)(146,210)(147,209)(148,203)(149,207)(150,206)(151,205)(152,204)(153,228)(154,232)(155,231)(156,230)(157,229)(158,238)(159,242)(160,241)(161,240)(162,239)(163,233)(164,237)(165,236)(166,235)(167,234)(168,213)(169,217)(170,216)(171,215)(172,214)(173,223)(174,227)(175,226)(176,225)(177,224)(178,218)(179,222)(180,221)(181,220)(182,219);;
s2 := (  3,129)(  4,128)(  5,132)(  6,131)(  7,130)(  8,124)(  9,123)( 10,127)( 11,126)( 12,125)( 13,134)( 14,133)( 15,137)( 16,136)( 17,135)( 18,144)( 19,143)( 20,147)( 21,146)( 22,145)( 23,139)( 24,138)( 25,142)( 26,141)( 27,140)( 28,149)( 29,148)( 30,152)( 31,151)( 32,150)( 33,174)( 34,173)( 35,177)( 36,176)( 37,175)( 38,169)( 39,168)( 40,172)( 41,171)( 42,170)( 43,179)( 44,178)( 45,182)( 46,181)( 47,180)( 48,159)( 49,158)( 50,162)( 51,161)( 52,160)( 53,154)( 54,153)( 55,157)( 56,156)( 57,155)( 58,164)( 59,163)( 60,167)( 61,166)( 62,165)( 63,219)( 64,218)( 65,222)( 66,221)( 67,220)( 68,214)( 69,213)( 70,217)( 71,216)( 72,215)( 73,224)( 74,223)( 75,227)( 76,226)( 77,225)( 78,234)( 79,233)( 80,237)( 81,236)( 82,235)( 83,229)( 84,228)( 85,232)( 86,231)( 87,230)( 88,239)( 89,238)( 90,242)( 91,241)( 92,240)( 93,189)( 94,188)( 95,192)( 96,191)( 97,190)( 98,184)( 99,183)(100,187)(101,186)(102,185)(103,194)(104,193)(105,197)(106,196)(107,195)(108,204)(109,203)(110,207)(111,206)(112,205)(113,199)(114,198)(115,202)(116,201)(117,200)(118,209)(119,208)(120,212)(121,211)(122,210);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(242)!(1,2);
s1 := Sym(242)!(  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)(123,183)(124,187)(125,186)(126,185)(127,184)(128,193)(129,197)(130,196)(131,195)(132,194)(133,188)(134,192)(135,191)(136,190)(137,189)(138,198)(139,202)(140,201)(141,200)(142,199)(143,208)(144,212)(145,211)(146,210)(147,209)(148,203)(149,207)(150,206)(151,205)(152,204)(153,228)(154,232)(155,231)(156,230)(157,229)(158,238)(159,242)(160,241)(161,240)(162,239)(163,233)(164,237)(165,236)(166,235)(167,234)(168,213)(169,217)(170,216)(171,215)(172,214)(173,223)(174,227)(175,226)(176,225)(177,224)(178,218)(179,222)(180,221)(181,220)(182,219);
s2 := Sym(242)!(  3,129)(  4,128)(  5,132)(  6,131)(  7,130)(  8,124)(  9,123)( 10,127)( 11,126)( 12,125)( 13,134)( 14,133)( 15,137)( 16,136)( 17,135)( 18,144)( 19,143)( 20,147)( 21,146)( 22,145)( 23,139)( 24,138)( 25,142)( 26,141)( 27,140)( 28,149)( 29,148)( 30,152)( 31,151)( 32,150)( 33,174)( 34,173)( 35,177)( 36,176)( 37,175)( 38,169)( 39,168)( 40,172)( 41,171)( 42,170)( 43,179)( 44,178)( 45,182)( 46,181)( 47,180)( 48,159)( 49,158)( 50,162)( 51,161)( 52,160)( 53,154)( 54,153)( 55,157)( 56,156)( 57,155)( 58,164)( 59,163)( 60,167)( 61,166)( 62,165)( 63,219)( 64,218)( 65,222)( 66,221)( 67,220)( 68,214)( 69,213)( 70,217)( 71,216)( 72,215)( 73,224)( 74,223)( 75,227)( 76,226)( 77,225)( 78,234)( 79,233)( 80,237)( 81,236)( 82,235)( 83,229)( 84,228)( 85,232)( 86,231)( 87,230)( 88,239)( 89,238)( 90,242)( 91,241)( 92,240)( 93,189)( 94,188)( 95,192)( 96,191)( 97,190)( 98,184)( 99,183)(100,187)(101,186)(102,185)(103,194)(104,193)(105,197)(106,196)(107,195)(108,204)(109,203)(110,207)(111,206)(112,205)(113,199)(114,198)(115,202)(116,201)(117,200)(118,209)(119,208)(120,212)(121,211)(122,210);
poly := sub<Sym(242)|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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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