Polytope of Type {244,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {244,2}*976
if this polytope has a name.
Group : SmallGroup(976,37)
Rank : 3
Schlafli Type : {244,2}
Number of vertices, edges, etc : 244, 244, 2
Order of s₀s₁s₂ : 244
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 :
   {244,2,2} of size 1952
Vertex Figure Of :
   {2,244,2} of size 1952
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {122,2}*488
   4-fold quotients : {61,2}*244
   61-fold quotients : {4,2}*16
   122-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {244,4}*1952, {488,2}*1952
Permutation Representation (GAP) :

s0 := (  2, 61)(  3, 60)(  4, 59)(  5, 58)(  6, 57)(  7, 56)(  8, 55)(  9, 54)
( 10, 53)( 11, 52)( 12, 51)( 13, 50)( 14, 49)( 15, 48)( 16, 47)( 17, 46)
( 18, 45)( 19, 44)( 20, 43)( 21, 42)( 22, 41)( 23, 40)( 24, 39)( 25, 38)
( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)( 31, 32)( 63,122)( 64,121)
( 65,120)( 66,119)( 67,118)( 68,117)( 69,116)( 70,115)( 71,114)( 72,113)
( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,107)( 79,106)( 80,105)
( 81,104)( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)( 88, 97)
( 89, 96)( 90, 95)( 91, 94)( 92, 93)(123,184)(124,244)(125,243)(126,242)
(127,241)(128,240)(129,239)(130,238)(131,237)(132,236)(133,235)(134,234)
(135,233)(136,232)(137,231)(138,230)(139,229)(140,228)(141,227)(142,226)
(143,225)(144,224)(145,223)(146,222)(147,221)(148,220)(149,219)(150,218)
(151,217)(152,216)(153,215)(154,214)(155,213)(156,212)(157,211)(158,210)
(159,209)(160,208)(161,207)(162,206)(163,205)(164,204)(165,203)(166,202)
(167,201)(168,200)(169,199)(170,198)(171,197)(172,196)(173,195)(174,194)
(175,193)(176,192)(177,191)(178,190)(179,189)(180,188)(181,187)(182,186)
(183,185);;
s1 := (  1,124)(  2,123)(  3,183)(  4,182)(  5,181)(  6,180)(  7,179)(  8,178)
(  9,177)( 10,176)( 11,175)( 12,174)( 13,173)( 14,172)( 15,171)( 16,170)
( 17,169)( 18,168)( 19,167)( 20,166)( 21,165)( 22,164)( 23,163)( 24,162)
( 25,161)( 26,160)( 27,159)( 28,158)( 29,157)( 30,156)( 31,155)( 32,154)
( 33,153)( 34,152)( 35,151)( 36,150)( 37,149)( 38,148)( 39,147)( 40,146)
( 41,145)( 42,144)( 43,143)( 44,142)( 45,141)( 46,140)( 47,139)( 48,138)
( 49,137)( 50,136)( 51,135)( 52,134)( 53,133)( 54,132)( 55,131)( 56,130)
( 57,129)( 58,128)( 59,127)( 60,126)( 61,125)( 62,185)( 63,184)( 64,244)
( 65,243)( 66,242)( 67,241)( 68,240)( 69,239)( 70,238)( 71,237)( 72,236)
( 73,235)( 74,234)( 75,233)( 76,232)( 77,231)( 78,230)( 79,229)( 80,228)
( 81,227)( 82,226)( 83,225)( 84,224)( 85,223)( 86,222)( 87,221)( 88,220)
( 89,219)( 90,218)( 91,217)( 92,216)( 93,215)( 94,214)( 95,213)( 96,212)
( 97,211)( 98,210)( 99,209)(100,208)(101,207)(102,206)(103,205)(104,204)
(105,203)(106,202)(107,201)(108,200)(109,199)(110,198)(111,197)(112,196)
(113,195)(114,194)(115,193)(116,192)(117,191)(118,190)(119,189)(120,188)
(121,187)(122,186);;
s2 := (245,246);;
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*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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(246)!(  2, 61)(  3, 60)(  4, 59)(  5, 58)(  6, 57)(  7, 56)(  8, 55)
(  9, 54)( 10, 53)( 11, 52)( 12, 51)( 13, 50)( 14, 49)( 15, 48)( 16, 47)
( 17, 46)( 18, 45)( 19, 44)( 20, 43)( 21, 42)( 22, 41)( 23, 40)( 24, 39)
( 25, 38)( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)( 31, 32)( 63,122)
( 64,121)( 65,120)( 66,119)( 67,118)( 68,117)( 69,116)( 70,115)( 71,114)
( 72,113)( 73,112)( 74,111)( 75,110)( 76,109)( 77,108)( 78,107)( 79,106)
( 80,105)( 81,104)( 82,103)( 83,102)( 84,101)( 85,100)( 86, 99)( 87, 98)
( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 92, 93)(123,184)(124,244)(125,243)
(126,242)(127,241)(128,240)(129,239)(130,238)(131,237)(132,236)(133,235)
(134,234)(135,233)(136,232)(137,231)(138,230)(139,229)(140,228)(141,227)
(142,226)(143,225)(144,224)(145,223)(146,222)(147,221)(148,220)(149,219)
(150,218)(151,217)(152,216)(153,215)(154,214)(155,213)(156,212)(157,211)
(158,210)(159,209)(160,208)(161,207)(162,206)(163,205)(164,204)(165,203)
(166,202)(167,201)(168,200)(169,199)(170,198)(171,197)(172,196)(173,195)
(174,194)(175,193)(176,192)(177,191)(178,190)(179,189)(180,188)(181,187)
(182,186)(183,185);
s1 := Sym(246)!(  1,124)(  2,123)(  3,183)(  4,182)(  5,181)(  6,180)(  7,179)
(  8,178)(  9,177)( 10,176)( 11,175)( 12,174)( 13,173)( 14,172)( 15,171)
( 16,170)( 17,169)( 18,168)( 19,167)( 20,166)( 21,165)( 22,164)( 23,163)
( 24,162)( 25,161)( 26,160)( 27,159)( 28,158)( 29,157)( 30,156)( 31,155)
( 32,154)( 33,153)( 34,152)( 35,151)( 36,150)( 37,149)( 38,148)( 39,147)
( 40,146)( 41,145)( 42,144)( 43,143)( 44,142)( 45,141)( 46,140)( 47,139)
( 48,138)( 49,137)( 50,136)( 51,135)( 52,134)( 53,133)( 54,132)( 55,131)
( 56,130)( 57,129)( 58,128)( 59,127)( 60,126)( 61,125)( 62,185)( 63,184)
( 64,244)( 65,243)( 66,242)( 67,241)( 68,240)( 69,239)( 70,238)( 71,237)
( 72,236)( 73,235)( 74,234)( 75,233)( 76,232)( 77,231)( 78,230)( 79,229)
( 80,228)( 81,227)( 82,226)( 83,225)( 84,224)( 85,223)( 86,222)( 87,221)
( 88,220)( 89,219)( 90,218)( 91,217)( 92,216)( 93,215)( 94,214)( 95,213)
( 96,212)( 97,211)( 98,210)( 99,209)(100,208)(101,207)(102,206)(103,205)
(104,204)(105,203)(106,202)(107,201)(108,200)(109,199)(110,198)(111,197)
(112,196)(113,195)(114,194)(115,193)(116,192)(117,191)(118,190)(119,189)
(120,188)(121,187)(122,186);
s2 := Sym(246)!(245,246);
poly := sub<Sym(246)|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*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*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope