Polytope of Type {22,22,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,22,2}*1936b
if this polytope has a name.
Group : SmallGroup(1936,164)
Rank : 4
Schlafli Type : {22,22,2}
Number of vertices, edges, etc : 22, 242, 22, 2
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 : {22,11,2}*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 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)(137,140)(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)(157,164)(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)(171,172)(178,187)(179,186)(180,185)(181,184)(182,183)(189,198)(190,197)(191,196)(192,195)(193,194)(200,209)(201,208)(202,207)(203,206)(204,205)(211,220)(212,219)(213,218)(214,217)(215,216)(222,231)(223,230)(224,229)(225,228)(226,227)(233,242)(234,241)(235,240)(236,239)(237,238);;
s1 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12,112)( 13,111)( 14,121)( 15,120)( 16,119)( 17,118)( 18,117)( 19,116)( 20,115)( 21,114)( 22,113)( 23,101)( 24,100)( 25,110)( 26,109)( 27,108)( 28,107)( 29,106)( 30,105)( 31,104)( 32,103)( 33,102)( 34, 90)( 35, 89)( 36, 99)( 37, 98)( 38, 97)( 39, 96)( 40, 95)( 41, 94)( 42, 93)( 43, 92)( 44, 91)( 45, 79)( 46, 78)( 47, 88)( 48, 87)( 49, 86)( 50, 85)( 51, 84)( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 68)( 57, 67)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)(122,123)(124,132)(125,131)(126,130)(127,129)(133,233)(134,232)(135,242)(136,241)(137,240)(138,239)(139,238)(140,237)(141,236)(142,235)(143,234)(144,222)(145,221)(146,231)(147,230)(148,229)(149,228)(150,227)(151,226)(152,225)(153,224)(154,223)(155,211)(156,210)(157,220)(158,219)(159,218)(160,217)(161,216)(162,215)(163,214)(164,213)(165,212)(166,200)(167,199)(168,209)(169,208)(170,207)(171,206)(172,205)(173,204)(174,203)(175,202)(176,201)(177,189)(178,188)(179,198)(180,197)(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190);;
s2 := ( 1,133)( 2,143)( 3,142)( 4,141)( 5,140)( 6,139)( 7,138)( 8,137)( 9,136)( 10,135)( 11,134)( 12,122)( 13,132)( 14,131)( 15,130)( 16,129)( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,232)( 24,242)( 25,241)( 26,240)( 27,239)( 28,238)( 29,237)( 30,236)( 31,235)( 32,234)( 33,233)( 34,221)( 35,231)( 36,230)( 37,229)( 38,228)( 39,227)( 40,226)( 41,225)( 42,224)( 43,223)( 44,222)( 45,210)( 46,220)( 47,219)( 48,218)( 49,217)( 50,216)( 51,215)( 52,214)( 53,213)( 54,212)( 55,211)( 56,199)( 57,209)( 58,208)( 59,207)( 60,206)( 61,205)( 62,204)( 63,203)( 64,202)( 65,201)( 66,200)( 67,188)( 68,198)( 69,197)( 70,196)( 71,195)( 72,194)( 73,193)( 74,192)( 75,191)( 76,190)( 77,189)( 78,177)( 79,187)( 80,186)( 81,185)( 82,184)( 83,183)( 84,182)( 85,181)( 86,180)( 87,179)( 88,178)( 89,166)( 90,176)( 91,175)( 92,174)( 93,173)( 94,172)( 95,171)( 96,170)( 97,169)( 98,168)( 99,167)(100,155)(101,165)(102,164)(103,163)(104,162)(105,161)(106,160)(107,159)(108,158)(109,157)(110,156)(111,144)(112,154)(113,153)(114,152)(115,151)(116,150)(117,149)(118,148)(119,147)(120,146)(121,145);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s0*s1*s0*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)(137,140)(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)(157,164)(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)(171,172)(178,187)(179,186)(180,185)(181,184)(182,183)(189,198)(190,197)(191,196)(192,195)(193,194)(200,209)(201,208)(202,207)(203,206)(204,205)(211,220)(212,219)(213,218)(214,217)(215,216)(222,231)(223,230)(224,229)(225,228)(226,227)(233,242)(234,241)(235,240)(236,239)(237,238);
s1 := Sym(244)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12,112)( 13,111)( 14,121)( 15,120)( 16,119)( 17,118)( 18,117)( 19,116)( 20,115)( 21,114)( 22,113)( 23,101)( 24,100)( 25,110)( 26,109)( 27,108)( 28,107)( 29,106)( 30,105)( 31,104)( 32,103)( 33,102)( 34, 90)( 35, 89)( 36, 99)( 37, 98)( 38, 97)( 39, 96)( 40, 95)( 41, 94)( 42, 93)( 43, 92)( 44, 91)( 45, 79)( 46, 78)( 47, 88)( 48, 87)( 49, 86)( 50, 85)( 51, 84)( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 68)( 57, 67)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)(122,123)(124,132)(125,131)(126,130)(127,129)(133,233)(134,232)(135,242)(136,241)(137,240)(138,239)(139,238)(140,237)(141,236)(142,235)(143,234)(144,222)(145,221)(146,231)(147,230)(148,229)(149,228)(150,227)(151,226)(152,225)(153,224)(154,223)(155,211)(156,210)(157,220)(158,219)(159,218)(160,217)(161,216)(162,215)(163,214)(164,213)(165,212)(166,200)(167,199)(168,209)(169,208)(170,207)(171,206)(172,205)(173,204)(174,203)(175,202)(176,201)(177,189)(178,188)(179,198)(180,197)(181,196)(182,195)(183,194)(184,193)(185,192)(186,191)(187,190);
s2 := Sym(244)!( 1,133)( 2,143)( 3,142)( 4,141)( 5,140)( 6,139)( 7,138)( 8,137)( 9,136)( 10,135)( 11,134)( 12,122)( 13,132)( 14,131)( 15,130)( 16,129)( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,232)( 24,242)( 25,241)( 26,240)( 27,239)( 28,238)( 29,237)( 30,236)( 31,235)( 32,234)( 33,233)( 34,221)( 35,231)( 36,230)( 37,229)( 38,228)( 39,227)( 40,226)( 41,225)( 42,224)( 43,223)( 44,222)( 45,210)( 46,220)( 47,219)( 48,218)( 49,217)( 50,216)( 51,215)( 52,214)( 53,213)( 54,212)( 55,211)( 56,199)( 57,209)( 58,208)( 59,207)( 60,206)( 61,205)( 62,204)( 63,203)( 64,202)( 65,201)( 66,200)( 67,188)( 68,198)( 69,197)( 70,196)( 71,195)( 72,194)( 73,193)( 74,192)( 75,191)( 76,190)( 77,189)( 78,177)( 79,187)( 80,186)( 81,185)( 82,184)( 83,183)( 84,182)( 85,181)( 86,180)( 87,179)( 88,178)( 89,166)( 90,176)( 91,175)( 92,174)( 93,173)( 94,172)( 95,171)( 96,170)( 97,169)( 98,168)( 99,167)(100,155)(101,165)(102,164)(103,163)(104,162)(105,161)(106,160)(107,159)(108,158)(109,157)(110,156)(111,144)(112,154)(113,153)(114,152)(115,151)(116,150)(117,149)(118,148)(119,147)(120,146)(121,145);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s2*s0*s1*s0*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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope