Polytope of Type {4,122}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,122}*976
Also Known As : {4,122|2}. if this polytope has another name.
Group : SmallGroup(976,39)
Rank : 3
Schlafli Type : {4,122}
Number of vertices, edges, etc : 4, 244, 122
Order of s0s1s2 : 244
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,122,2} of size 1952
Vertex Figure Of :
{2,4,122} of size 1952
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,122}*488
4-fold quotients : {2,61}*244
61-fold quotients : {4,2}*16
122-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,244}*1952, {8,122}*1952
Permutation Representation (GAP) :
s0 := (123,184)(124,185)(125,186)(126,187)(127,188)(128,189)(129,190)(130,191)
(131,192)(132,193)(133,194)(134,195)(135,196)(136,197)(137,198)(138,199)
(139,200)(140,201)(141,202)(142,203)(143,204)(144,205)(145,206)(146,207)
(147,208)(148,209)(149,210)(150,211)(151,212)(152,213)(153,214)(154,215)
(155,216)(156,217)(157,218)(158,219)(159,220)(160,221)(161,222)(162,223)
(163,224)(164,225)(165,226)(166,227)(167,228)(168,229)(169,230)(170,231)
(171,232)(172,233)(173,234)(174,235)(175,236)(176,237)(177,238)(178,239)
(179,240)(180,241)(181,242)(182,243)(183,244);;
s1 := ( 1,123)( 2,183)( 3,182)( 4,181)( 5,180)( 6,179)( 7,178)( 8,177)
( 9,176)( 10,175)( 11,174)( 12,173)( 13,172)( 14,171)( 15,170)( 16,169)
( 17,168)( 18,167)( 19,166)( 20,165)( 21,164)( 22,163)( 23,162)( 24,161)
( 25,160)( 26,159)( 27,158)( 28,157)( 29,156)( 30,155)( 31,154)( 32,153)
( 33,152)( 34,151)( 35,150)( 36,149)( 37,148)( 38,147)( 39,146)( 40,145)
( 41,144)( 42,143)( 43,142)( 44,141)( 45,140)( 46,139)( 47,138)( 48,137)
( 49,136)( 50,135)( 51,134)( 52,133)( 53,132)( 54,131)( 55,130)( 56,129)
( 57,128)( 58,127)( 59,126)( 60,125)( 61,124)( 62,184)( 63,244)( 64,243)
( 65,242)( 66,241)( 67,240)( 68,239)( 69,238)( 70,237)( 71,236)( 72,235)
( 73,234)( 74,233)( 75,232)( 76,231)( 77,230)( 78,229)( 79,228)( 80,227)
( 81,226)( 82,225)( 83,224)( 84,223)( 85,222)( 86,221)( 87,220)( 88,219)
( 89,218)( 90,217)( 91,216)( 92,215)( 93,214)( 94,213)( 95,212)( 96,211)
( 97,210)( 98,209)( 99,208)(100,207)(101,206)(102,205)(103,204)(104,203)
(105,202)(106,201)(107,200)(108,199)(109,198)(110,197)(111,196)(112,195)
(113,194)(114,193)(115,192)(116,191)(117,190)(118,189)(119,188)(120,187)
(121,186)(122,185);;
s2 := ( 1, 2)( 3, 61)( 4, 60)( 5, 59)( 6, 58)( 7, 57)( 8, 56)( 9, 55)
( 10, 54)( 11, 53)( 12, 52)( 13, 51)( 14, 50)( 15, 49)( 16, 48)( 17, 47)
( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)( 24, 40)( 25, 39)
( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 31, 33)( 62, 63)( 64,122)
( 65,121)( 66,120)( 67,119)( 68,118)( 69,117)( 70,116)( 71,115)( 72,114)
( 73,113)( 74,112)( 75,111)( 76,110)( 77,109)( 78,108)( 79,107)( 80,106)
( 81,105)( 82,104)( 83,103)( 84,102)( 85,101)( 86,100)( 87, 99)( 88, 98)
( 89, 97)( 90, 96)( 91, 95)( 92, 94)(123,124)(125,183)(126,182)(127,181)
(128,180)(129,179)(130,178)(131,177)(132,176)(133,175)(134,174)(135,173)
(136,172)(137,171)(138,170)(139,169)(140,168)(141,167)(142,166)(143,165)
(144,164)(145,163)(146,162)(147,161)(148,160)(149,159)(150,158)(151,157)
(152,156)(153,155)(184,185)(186,244)(187,243)(188,242)(189,241)(190,240)
(191,239)(192,238)(193,237)(194,236)(195,235)(196,234)(197,233)(198,232)
(199,231)(200,230)(201,229)(202,228)(203,227)(204,226)(205,225)(206,224)
(207,223)(208,222)(209,221)(210,220)(211,219)(212,218)(213,217)(214,216);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!(123,184)(124,185)(125,186)(126,187)(127,188)(128,189)(129,190)
(130,191)(131,192)(132,193)(133,194)(134,195)(135,196)(136,197)(137,198)
(138,199)(139,200)(140,201)(141,202)(142,203)(143,204)(144,205)(145,206)
(146,207)(147,208)(148,209)(149,210)(150,211)(151,212)(152,213)(153,214)
(154,215)(155,216)(156,217)(157,218)(158,219)(159,220)(160,221)(161,222)
(162,223)(163,224)(164,225)(165,226)(166,227)(167,228)(168,229)(169,230)
(170,231)(171,232)(172,233)(173,234)(174,235)(175,236)(176,237)(177,238)
(178,239)(179,240)(180,241)(181,242)(182,243)(183,244);
s1 := Sym(244)!( 1,123)( 2,183)( 3,182)( 4,181)( 5,180)( 6,179)( 7,178)
( 8,177)( 9,176)( 10,175)( 11,174)( 12,173)( 13,172)( 14,171)( 15,170)
( 16,169)( 17,168)( 18,167)( 19,166)( 20,165)( 21,164)( 22,163)( 23,162)
( 24,161)( 25,160)( 26,159)( 27,158)( 28,157)( 29,156)( 30,155)( 31,154)
( 32,153)( 33,152)( 34,151)( 35,150)( 36,149)( 37,148)( 38,147)( 39,146)
( 40,145)( 41,144)( 42,143)( 43,142)( 44,141)( 45,140)( 46,139)( 47,138)
( 48,137)( 49,136)( 50,135)( 51,134)( 52,133)( 53,132)( 54,131)( 55,130)
( 56,129)( 57,128)( 58,127)( 59,126)( 60,125)( 61,124)( 62,184)( 63,244)
( 64,243)( 65,242)( 66,241)( 67,240)( 68,239)( 69,238)( 70,237)( 71,236)
( 72,235)( 73,234)( 74,233)( 75,232)( 76,231)( 77,230)( 78,229)( 79,228)
( 80,227)( 81,226)( 82,225)( 83,224)( 84,223)( 85,222)( 86,221)( 87,220)
( 88,219)( 89,218)( 90,217)( 91,216)( 92,215)( 93,214)( 94,213)( 95,212)
( 96,211)( 97,210)( 98,209)( 99,208)(100,207)(101,206)(102,205)(103,204)
(104,203)(105,202)(106,201)(107,200)(108,199)(109,198)(110,197)(111,196)
(112,195)(113,194)(114,193)(115,192)(116,191)(117,190)(118,189)(119,188)
(120,187)(121,186)(122,185);
s2 := Sym(244)!( 1, 2)( 3, 61)( 4, 60)( 5, 59)( 6, 58)( 7, 57)( 8, 56)
( 9, 55)( 10, 54)( 11, 53)( 12, 52)( 13, 51)( 14, 50)( 15, 49)( 16, 48)
( 17, 47)( 18, 46)( 19, 45)( 20, 44)( 21, 43)( 22, 42)( 23, 41)( 24, 40)
( 25, 39)( 26, 38)( 27, 37)( 28, 36)( 29, 35)( 30, 34)( 31, 33)( 62, 63)
( 64,122)( 65,121)( 66,120)( 67,119)( 68,118)( 69,117)( 70,116)( 71,115)
( 72,114)( 73,113)( 74,112)( 75,111)( 76,110)( 77,109)( 78,108)( 79,107)
( 80,106)( 81,105)( 82,104)( 83,103)( 84,102)( 85,101)( 86,100)( 87, 99)
( 88, 98)( 89, 97)( 90, 96)( 91, 95)( 92, 94)(123,124)(125,183)(126,182)
(127,181)(128,180)(129,179)(130,178)(131,177)(132,176)(133,175)(134,174)
(135,173)(136,172)(137,171)(138,170)(139,169)(140,168)(141,167)(142,166)
(143,165)(144,164)(145,163)(146,162)(147,161)(148,160)(149,159)(150,158)
(151,157)(152,156)(153,155)(184,185)(186,244)(187,243)(188,242)(189,241)
(190,240)(191,239)(192,238)(193,237)(194,236)(195,235)(196,234)(197,233)
(198,232)(199,231)(200,230)(201,229)(202,228)(203,227)(204,226)(205,225)
(206,224)(207,223)(208,222)(209,221)(210,220)(211,219)(212,218)(213,217)
(214,216);
poly := sub<Sym(244)|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, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope