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Polytope of Type {2,240,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,240,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,203900)
Rank : 4
Schlafli Type : {2,240,2}
Number of vertices, edges, etc : 2, 240, 240, 2
Order of s0s1s2s3 : 240
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
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 : {2,120,2}*960
   3-fold quotients : {2,80,2}*640
   4-fold quotients : {2,60,2}*480
   5-fold quotients : {2,48,2}*384
   6-fold quotients : {2,40,2}*320
   8-fold quotients : {2,30,2}*240
   10-fold quotients : {2,24,2}*192
   12-fold quotients : {2,20,2}*160
   15-fold quotients : {2,16,2}*128
   16-fold quotients : {2,15,2}*120
   20-fold quotients : {2,12,2}*96
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {2,8,2}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,4,2}*32
   80-fold quotients : {2,3,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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);;
s3 := (243,244);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(244)!(1,2);
s1 := Sym(244)!(  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(244)!(  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);
s3 := Sym(244)!(243,244);
poly := sub<Sym(244)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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