Polytope of Type {2,22,22}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,22}*1936c
if this polytope has a name.
Group : SmallGroup(1936,164)
Rank : 4
Schlafli Type : {2,22,22}
Number of vertices, edges, etc : 2, 22, 242, 22
Order of s0s1s2s3 : 22
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 : {2,11,22}*968
11-fold quotients : {2,22,2}*176
22-fold quotients : {2,11,2}*88
121-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 14,113)( 15,123)( 16,122)
( 17,121)( 18,120)( 19,119)( 20,118)( 21,117)( 22,116)( 23,115)( 24,114)
( 25,102)( 26,112)( 27,111)( 28,110)( 29,109)( 30,108)( 31,107)( 32,106)
( 33,105)( 34,104)( 35,103)( 36, 91)( 37,101)( 38,100)( 39, 99)( 40, 98)
( 41, 97)( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 80)( 48, 90)
( 49, 89)( 50, 88)( 51, 87)( 52, 86)( 53, 85)( 54, 84)( 55, 83)( 56, 82)
( 57, 81)( 58, 69)( 59, 79)( 60, 78)( 61, 77)( 62, 76)( 63, 75)( 64, 74)
( 65, 73)( 66, 72)( 67, 71)( 68, 70)(125,134)(126,133)(127,132)(128,131)
(129,130)(135,234)(136,244)(137,243)(138,242)(139,241)(140,240)(141,239)
(142,238)(143,237)(144,236)(145,235)(146,223)(147,233)(148,232)(149,231)
(150,230)(151,229)(152,228)(153,227)(154,226)(155,225)(156,224)(157,212)
(158,222)(159,221)(160,220)(161,219)(162,218)(163,217)(164,216)(165,215)
(166,214)(167,213)(168,201)(169,211)(170,210)(171,209)(172,208)(173,207)
(174,206)(175,205)(176,204)(177,203)(178,202)(179,190)(180,200)(181,199)
(182,198)(183,197)(184,196)(185,195)(186,194)(187,193)(188,192)(189,191);;
s2 := ( 3,136)( 4,135)( 5,145)( 6,144)( 7,143)( 8,142)( 9,141)( 10,140)
( 11,139)( 12,138)( 13,137)( 14,125)( 15,124)( 16,134)( 17,133)( 18,132)
( 19,131)( 20,130)( 21,129)( 22,128)( 23,127)( 24,126)( 25,235)( 26,234)
( 27,244)( 28,243)( 29,242)( 30,241)( 31,240)( 32,239)( 33,238)( 34,237)
( 35,236)( 36,224)( 37,223)( 38,233)( 39,232)( 40,231)( 41,230)( 42,229)
( 43,228)( 44,227)( 45,226)( 46,225)( 47,213)( 48,212)( 49,222)( 50,221)
( 51,220)( 52,219)( 53,218)( 54,217)( 55,216)( 56,215)( 57,214)( 58,202)
( 59,201)( 60,211)( 61,210)( 62,209)( 63,208)( 64,207)( 65,206)( 66,205)
( 67,204)( 68,203)( 69,191)( 70,190)( 71,200)( 72,199)( 73,198)( 74,197)
( 75,196)( 76,195)( 77,194)( 78,193)( 79,192)( 80,180)( 81,179)( 82,189)
( 83,188)( 84,187)( 85,186)( 86,185)( 87,184)( 88,183)( 89,182)( 90,181)
( 91,169)( 92,168)( 93,178)( 94,177)( 95,176)( 96,175)( 97,174)( 98,173)
( 99,172)(100,171)(101,170)(102,158)(103,157)(104,167)(105,166)(106,165)
(107,164)(108,163)(109,162)(110,161)(111,160)(112,159)(113,147)(114,146)
(115,156)(116,155)(117,154)(118,153)(119,152)(120,151)(121,150)(122,149)
(123,148);;
s3 := ( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 15, 24)( 16, 23)( 17, 22)
( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 37, 46)
( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)( 51, 54)
( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 70, 79)( 71, 78)
( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)
( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(103,112)(104,111)(105,110)
(106,109)(107,108)(114,123)(115,122)(116,121)(117,120)(118,119)(125,134)
(126,133)(127,132)(128,131)(129,130)(136,145)(137,144)(138,143)(139,142)
(140,141)(147,156)(148,155)(149,154)(150,153)(151,152)(158,167)(159,166)
(160,165)(161,164)(162,163)(169,178)(170,177)(171,176)(172,175)(173,174)
(180,189)(181,188)(182,187)(183,186)(184,185)(191,200)(192,199)(193,198)
(194,197)(195,196)(202,211)(203,210)(204,209)(205,208)(206,207)(213,222)
(214,221)(215,220)(216,219)(217,218)(224,233)(225,232)(226,231)(227,230)
(228,229)(235,244)(236,243)(237,242)(238,241)(239,240);;
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,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*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, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 14,113)( 15,123)
( 16,122)( 17,121)( 18,120)( 19,119)( 20,118)( 21,117)( 22,116)( 23,115)
( 24,114)( 25,102)( 26,112)( 27,111)( 28,110)( 29,109)( 30,108)( 31,107)
( 32,106)( 33,105)( 34,104)( 35,103)( 36, 91)( 37,101)( 38,100)( 39, 99)
( 40, 98)( 41, 97)( 42, 96)( 43, 95)( 44, 94)( 45, 93)( 46, 92)( 47, 80)
( 48, 90)( 49, 89)( 50, 88)( 51, 87)( 52, 86)( 53, 85)( 54, 84)( 55, 83)
( 56, 82)( 57, 81)( 58, 69)( 59, 79)( 60, 78)( 61, 77)( 62, 76)( 63, 75)
( 64, 74)( 65, 73)( 66, 72)( 67, 71)( 68, 70)(125,134)(126,133)(127,132)
(128,131)(129,130)(135,234)(136,244)(137,243)(138,242)(139,241)(140,240)
(141,239)(142,238)(143,237)(144,236)(145,235)(146,223)(147,233)(148,232)
(149,231)(150,230)(151,229)(152,228)(153,227)(154,226)(155,225)(156,224)
(157,212)(158,222)(159,221)(160,220)(161,219)(162,218)(163,217)(164,216)
(165,215)(166,214)(167,213)(168,201)(169,211)(170,210)(171,209)(172,208)
(173,207)(174,206)(175,205)(176,204)(177,203)(178,202)(179,190)(180,200)
(181,199)(182,198)(183,197)(184,196)(185,195)(186,194)(187,193)(188,192)
(189,191);
s2 := Sym(244)!( 3,136)( 4,135)( 5,145)( 6,144)( 7,143)( 8,142)( 9,141)
( 10,140)( 11,139)( 12,138)( 13,137)( 14,125)( 15,124)( 16,134)( 17,133)
( 18,132)( 19,131)( 20,130)( 21,129)( 22,128)( 23,127)( 24,126)( 25,235)
( 26,234)( 27,244)( 28,243)( 29,242)( 30,241)( 31,240)( 32,239)( 33,238)
( 34,237)( 35,236)( 36,224)( 37,223)( 38,233)( 39,232)( 40,231)( 41,230)
( 42,229)( 43,228)( 44,227)( 45,226)( 46,225)( 47,213)( 48,212)( 49,222)
( 50,221)( 51,220)( 52,219)( 53,218)( 54,217)( 55,216)( 56,215)( 57,214)
( 58,202)( 59,201)( 60,211)( 61,210)( 62,209)( 63,208)( 64,207)( 65,206)
( 66,205)( 67,204)( 68,203)( 69,191)( 70,190)( 71,200)( 72,199)( 73,198)
( 74,197)( 75,196)( 76,195)( 77,194)( 78,193)( 79,192)( 80,180)( 81,179)
( 82,189)( 83,188)( 84,187)( 85,186)( 86,185)( 87,184)( 88,183)( 89,182)
( 90,181)( 91,169)( 92,168)( 93,178)( 94,177)( 95,176)( 96,175)( 97,174)
( 98,173)( 99,172)(100,171)(101,170)(102,158)(103,157)(104,167)(105,166)
(106,165)(107,164)(108,163)(109,162)(110,161)(111,160)(112,159)(113,147)
(114,146)(115,156)(116,155)(117,154)(118,153)(119,152)(120,151)(121,150)
(122,149)(123,148);
s3 := Sym(244)!( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 15, 24)( 16, 23)
( 17, 22)( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)
( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)
( 51, 54)( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 70, 79)
( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)
( 85, 86)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(103,112)(104,111)
(105,110)(106,109)(107,108)(114,123)(115,122)(116,121)(117,120)(118,119)
(125,134)(126,133)(127,132)(128,131)(129,130)(136,145)(137,144)(138,143)
(139,142)(140,141)(147,156)(148,155)(149,154)(150,153)(151,152)(158,167)
(159,166)(160,165)(161,164)(162,163)(169,178)(170,177)(171,176)(172,175)
(173,174)(180,189)(181,188)(182,187)(183,186)(184,185)(191,200)(192,199)
(193,198)(194,197)(195,196)(202,211)(203,210)(204,209)(205,208)(206,207)
(213,222)(214,221)(215,220)(216,219)(217,218)(224,233)(225,232)(226,231)
(227,230)(228,229)(235,244)(236,243)(237,242)(238,241)(239,240);
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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope