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Polytope of Type {2,6,80}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,80}*1920
if this polytope has a name.
Group : SmallGroup(1920,203907)
Rank : 4
Schlafli Type : {2,6,80}
Number of vertices, edges, etc : 2, 6, 240, 80
Order of s0s1s2s3 : 240
Order of s0s1s2s3s2s1 : 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 : {2,6,40}*960
   3-fold quotients : {2,2,80}*640
   4-fold quotients : {2,6,20}*480a
   5-fold quotients : {2,6,16}*384
   6-fold quotients : {2,2,40}*320
   8-fold quotients : {2,6,10}*240
   10-fold quotients : {2,6,8}*192
   12-fold quotients : {2,2,20}*160
   15-fold quotients : {2,2,16}*128
   20-fold quotients : {2,6,4}*96a
   24-fold quotients : {2,2,10}*80
   30-fold quotients : {2,2,8}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,2,4}*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 := (  8, 13)(  9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)( 25, 30)
( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 53, 58)
( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 68, 73)( 69, 74)( 70, 75)( 71, 76)
( 72, 77)( 83, 88)( 84, 89)( 85, 90)( 86, 91)( 87, 92)( 98,103)( 99,104)
(100,105)(101,106)(102,107)(113,118)(114,119)(115,120)(116,121)(117,122)
(128,133)(129,134)(130,135)(131,136)(132,137)(143,148)(144,149)(145,150)
(146,151)(147,152)(158,163)(159,164)(160,165)(161,166)(162,167)(173,178)
(174,179)(175,180)(176,181)(177,182)(188,193)(189,194)(190,195)(191,196)
(192,197)(203,208)(204,209)(205,210)(206,211)(207,212)(218,223)(219,224)
(220,225)(221,226)(222,227)(233,238)(234,239)(235,240)(236,241)(237,242);;
s2 := (  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 17)( 15, 16)( 18, 23)
( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 29, 32)( 30, 31)( 33, 53)( 34, 57)
( 35, 56)( 36, 55)( 37, 54)( 38, 48)( 39, 52)( 40, 51)( 41, 50)( 42, 49)
( 43, 58)( 44, 62)( 45, 61)( 46, 60)( 47, 59)( 63, 98)( 64,102)( 65,101)
( 66,100)( 67, 99)( 68, 93)( 69, 97)( 70, 96)( 71, 95)( 72, 94)( 73,103)
( 74,107)( 75,106)( 76,105)( 77,104)( 78,113)( 79,117)( 80,116)( 81,115)
( 82,114)( 83,108)( 84,112)( 85,111)( 86,110)( 87,109)( 88,118)( 89,122)
( 90,121)( 91,120)( 92,119)(123,188)(124,192)(125,191)(126,190)(127,189)
(128,183)(129,187)(130,186)(131,185)(132,184)(133,193)(134,197)(135,196)
(136,195)(137,194)(138,203)(139,207)(140,206)(141,205)(142,204)(143,198)
(144,202)(145,201)(146,200)(147,199)(148,208)(149,212)(150,211)(151,210)
(152,209)(153,233)(154,237)(155,236)(156,235)(157,234)(158,228)(159,232)
(160,231)(161,230)(162,229)(163,238)(164,242)(165,241)(166,240)(167,239)
(168,218)(169,222)(170,221)(171,220)(172,219)(173,213)(174,217)(175,216)
(176,215)(177,214)(178,223)(179,227)(180,226)(181,225)(182,224);;
s3 := (  3,124)(  4,123)(  5,127)(  6,126)(  7,125)(  8,129)(  9,128)( 10,132)
( 11,131)( 12,130)( 13,134)( 14,133)( 15,137)( 16,136)( 17,135)( 18,139)
( 19,138)( 20,142)( 21,141)( 22,140)( 23,144)( 24,143)( 25,147)( 26,146)
( 27,145)( 28,149)( 29,148)( 30,152)( 31,151)( 32,150)( 33,169)( 34,168)
( 35,172)( 36,171)( 37,170)( 38,174)( 39,173)( 40,177)( 41,176)( 42,175)
( 43,179)( 44,178)( 45,182)( 46,181)( 47,180)( 48,154)( 49,153)( 50,157)
( 51,156)( 52,155)( 53,159)( 54,158)( 55,162)( 56,161)( 57,160)( 58,164)
( 59,163)( 60,167)( 61,166)( 62,165)( 63,214)( 64,213)( 65,217)( 66,216)
( 67,215)( 68,219)( 69,218)( 70,222)( 71,221)( 72,220)( 73,224)( 74,223)
( 75,227)( 76,226)( 77,225)( 78,229)( 79,228)( 80,232)( 81,231)( 82,230)
( 83,234)( 84,233)( 85,237)( 86,236)( 87,235)( 88,239)( 89,238)( 90,242)
( 91,241)( 92,240)( 93,184)( 94,183)( 95,187)( 96,186)( 97,185)( 98,189)
( 99,188)(100,192)(101,191)(102,190)(103,194)(104,193)(105,197)(106,196)
(107,195)(108,199)(109,198)(110,202)(111,201)(112,200)(113,204)(114,203)
(115,207)(116,206)(117,205)(118,209)(119,208)(120,212)(121,211)(122,210);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(242)!(1,2);
s1 := Sym(242)!(  8, 13)(  9, 14)( 10, 15)( 11, 16)( 12, 17)( 23, 28)( 24, 29)
( 25, 30)( 26, 31)( 27, 32)( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)
( 53, 58)( 54, 59)( 55, 60)( 56, 61)( 57, 62)( 68, 73)( 69, 74)( 70, 75)
( 71, 76)( 72, 77)( 83, 88)( 84, 89)( 85, 90)( 86, 91)( 87, 92)( 98,103)
( 99,104)(100,105)(101,106)(102,107)(113,118)(114,119)(115,120)(116,121)
(117,122)(128,133)(129,134)(130,135)(131,136)(132,137)(143,148)(144,149)
(145,150)(146,151)(147,152)(158,163)(159,164)(160,165)(161,166)(162,167)
(173,178)(174,179)(175,180)(176,181)(177,182)(188,193)(189,194)(190,195)
(191,196)(192,197)(203,208)(204,209)(205,210)(206,211)(207,212)(218,223)
(219,224)(220,225)(221,226)(222,227)(233,238)(234,239)(235,240)(236,241)
(237,242);
s2 := Sym(242)!(  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 17)( 15, 16)
( 18, 23)( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 29, 32)( 30, 31)( 33, 53)
( 34, 57)( 35, 56)( 36, 55)( 37, 54)( 38, 48)( 39, 52)( 40, 51)( 41, 50)
( 42, 49)( 43, 58)( 44, 62)( 45, 61)( 46, 60)( 47, 59)( 63, 98)( 64,102)
( 65,101)( 66,100)( 67, 99)( 68, 93)( 69, 97)( 70, 96)( 71, 95)( 72, 94)
( 73,103)( 74,107)( 75,106)( 76,105)( 77,104)( 78,113)( 79,117)( 80,116)
( 81,115)( 82,114)( 83,108)( 84,112)( 85,111)( 86,110)( 87,109)( 88,118)
( 89,122)( 90,121)( 91,120)( 92,119)(123,188)(124,192)(125,191)(126,190)
(127,189)(128,183)(129,187)(130,186)(131,185)(132,184)(133,193)(134,197)
(135,196)(136,195)(137,194)(138,203)(139,207)(140,206)(141,205)(142,204)
(143,198)(144,202)(145,201)(146,200)(147,199)(148,208)(149,212)(150,211)
(151,210)(152,209)(153,233)(154,237)(155,236)(156,235)(157,234)(158,228)
(159,232)(160,231)(161,230)(162,229)(163,238)(164,242)(165,241)(166,240)
(167,239)(168,218)(169,222)(170,221)(171,220)(172,219)(173,213)(174,217)
(175,216)(176,215)(177,214)(178,223)(179,227)(180,226)(181,225)(182,224);
s3 := Sym(242)!(  3,124)(  4,123)(  5,127)(  6,126)(  7,125)(  8,129)(  9,128)
( 10,132)( 11,131)( 12,130)( 13,134)( 14,133)( 15,137)( 16,136)( 17,135)
( 18,139)( 19,138)( 20,142)( 21,141)( 22,140)( 23,144)( 24,143)( 25,147)
( 26,146)( 27,145)( 28,149)( 29,148)( 30,152)( 31,151)( 32,150)( 33,169)
( 34,168)( 35,172)( 36,171)( 37,170)( 38,174)( 39,173)( 40,177)( 41,176)
( 42,175)( 43,179)( 44,178)( 45,182)( 46,181)( 47,180)( 48,154)( 49,153)
( 50,157)( 51,156)( 52,155)( 53,159)( 54,158)( 55,162)( 56,161)( 57,160)
( 58,164)( 59,163)( 60,167)( 61,166)( 62,165)( 63,214)( 64,213)( 65,217)
( 66,216)( 67,215)( 68,219)( 69,218)( 70,222)( 71,221)( 72,220)( 73,224)
( 74,223)( 75,227)( 76,226)( 77,225)( 78,229)( 79,228)( 80,232)( 81,231)
( 82,230)( 83,234)( 84,233)( 85,237)( 86,236)( 87,235)( 88,239)( 89,238)
( 90,242)( 91,241)( 92,240)( 93,184)( 94,183)( 95,187)( 96,186)( 97,185)
( 98,189)( 99,188)(100,192)(101,191)(102,190)(103,194)(104,193)(105,197)
(106,196)(107,195)(108,199)(109,198)(110,202)(111,201)(112,200)(113,204)
(114,203)(115,207)(116,206)(117,205)(118,209)(119,208)(120,212)(121,211)
(122,210);
poly := sub<Sym(242)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

to this polytope