Polytope of Type {2,22,22}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,22}*1936b
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 : {2,22,11}*968
11-fold quotients : {2,2,22}*176
22-fold quotients : {2,2,11}*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)( 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);;
s2 := ( 3, 4)( 5, 13)( 6, 12)( 7, 11)( 8, 10)( 14,114)( 15,113)( 16,123)
( 17,122)( 18,121)( 19,120)( 20,119)( 21,118)( 22,117)( 23,116)( 24,115)
( 25,103)( 26,102)( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)( 32,107)
( 33,106)( 34,105)( 35,104)( 36, 92)( 37, 91)( 38,101)( 39,100)( 40, 99)
( 41, 98)( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 81)( 48, 80)
( 49, 90)( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)
( 57, 82)( 58, 70)( 59, 69)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)
( 65, 74)( 66, 73)( 67, 72)( 68, 71)(124,125)(126,134)(127,133)(128,132)
(129,131)(135,235)(136,234)(137,244)(138,243)(139,242)(140,241)(141,240)
(142,239)(143,238)(144,237)(145,236)(146,224)(147,223)(148,233)(149,232)
(150,231)(151,230)(152,229)(153,228)(154,227)(155,226)(156,225)(157,213)
(158,212)(159,222)(160,221)(161,220)(162,219)(163,218)(164,217)(165,216)
(166,215)(167,214)(168,202)(169,201)(170,211)(171,210)(172,209)(173,208)
(174,207)(175,206)(176,205)(177,204)(178,203)(179,191)(180,190)(181,200)
(182,199)(183,198)(184,197)(185,196)(186,195)(187,194)(188,193)(189,192);;
s3 := ( 3,135)( 4,145)( 5,144)( 6,143)( 7,142)( 8,141)( 9,140)( 10,139)
( 11,138)( 12,137)( 13,136)( 14,124)( 15,134)( 16,133)( 17,132)( 18,131)
( 19,130)( 20,129)( 21,128)( 22,127)( 23,126)( 24,125)( 25,234)( 26,244)
( 27,243)( 28,242)( 29,241)( 30,240)( 31,239)( 32,238)( 33,237)( 34,236)
( 35,235)( 36,223)( 37,233)( 38,232)( 39,231)( 40,230)( 41,229)( 42,228)
( 43,227)( 44,226)( 45,225)( 46,224)( 47,212)( 48,222)( 49,221)( 50,220)
( 51,219)( 52,218)( 53,217)( 54,216)( 55,215)( 56,214)( 57,213)( 58,201)
( 59,211)( 60,210)( 61,209)( 62,208)( 63,207)( 64,206)( 65,205)( 66,204)
( 67,203)( 68,202)( 69,190)( 70,200)( 71,199)( 72,198)( 73,197)( 74,196)
( 75,195)( 76,194)( 77,193)( 78,192)( 79,191)( 80,179)( 81,189)( 82,188)
( 83,187)( 84,186)( 85,185)( 86,184)( 87,183)( 88,182)( 89,181)( 90,180)
( 91,168)( 92,178)( 93,177)( 94,176)( 95,175)( 96,174)( 97,173)( 98,172)
( 99,171)(100,170)(101,169)(102,157)(103,167)(104,166)(105,165)(106,164)
(107,163)(108,162)(109,161)(110,160)(111,159)(112,158)(113,146)(114,156)
(115,155)(116,154)(117,153)(118,152)(119,151)(120,150)(121,149)(122,148)
(123,147);;
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*s1*s2*s3*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(244)!(1,2);
s1 := 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);
s2 := Sym(244)!( 3, 4)( 5, 13)( 6, 12)( 7, 11)( 8, 10)( 14,114)( 15,113)
( 16,123)( 17,122)( 18,121)( 19,120)( 20,119)( 21,118)( 22,117)( 23,116)
( 24,115)( 25,103)( 26,102)( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)
( 32,107)( 33,106)( 34,105)( 35,104)( 36, 92)( 37, 91)( 38,101)( 39,100)
( 40, 99)( 41, 98)( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 81)
( 48, 80)( 49, 90)( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)
( 56, 83)( 57, 82)( 58, 70)( 59, 69)( 60, 79)( 61, 78)( 62, 77)( 63, 76)
( 64, 75)( 65, 74)( 66, 73)( 67, 72)( 68, 71)(124,125)(126,134)(127,133)
(128,132)(129,131)(135,235)(136,234)(137,244)(138,243)(139,242)(140,241)
(141,240)(142,239)(143,238)(144,237)(145,236)(146,224)(147,223)(148,233)
(149,232)(150,231)(151,230)(152,229)(153,228)(154,227)(155,226)(156,225)
(157,213)(158,212)(159,222)(160,221)(161,220)(162,219)(163,218)(164,217)
(165,216)(166,215)(167,214)(168,202)(169,201)(170,211)(171,210)(172,209)
(173,208)(174,207)(175,206)(176,205)(177,204)(178,203)(179,191)(180,190)
(181,200)(182,199)(183,198)(184,197)(185,196)(186,195)(187,194)(188,193)
(189,192);
s3 := Sym(244)!( 3,135)( 4,145)( 5,144)( 6,143)( 7,142)( 8,141)( 9,140)
( 10,139)( 11,138)( 12,137)( 13,136)( 14,124)( 15,134)( 16,133)( 17,132)
( 18,131)( 19,130)( 20,129)( 21,128)( 22,127)( 23,126)( 24,125)( 25,234)
( 26,244)( 27,243)( 28,242)( 29,241)( 30,240)( 31,239)( 32,238)( 33,237)
( 34,236)( 35,235)( 36,223)( 37,233)( 38,232)( 39,231)( 40,230)( 41,229)
( 42,228)( 43,227)( 44,226)( 45,225)( 46,224)( 47,212)( 48,222)( 49,221)
( 50,220)( 51,219)( 52,218)( 53,217)( 54,216)( 55,215)( 56,214)( 57,213)
( 58,201)( 59,211)( 60,210)( 61,209)( 62,208)( 63,207)( 64,206)( 65,205)
( 66,204)( 67,203)( 68,202)( 69,190)( 70,200)( 71,199)( 72,198)( 73,197)
( 74,196)( 75,195)( 76,194)( 77,193)( 78,192)( 79,191)( 80,179)( 81,189)
( 82,188)( 83,187)( 84,186)( 85,185)( 86,184)( 87,183)( 88,182)( 89,181)
( 90,180)( 91,168)( 92,178)( 93,177)( 94,176)( 95,175)( 96,174)( 97,173)
( 98,172)( 99,171)(100,170)(101,169)(102,157)(103,167)(104,166)(105,165)
(106,164)(107,163)(108,162)(109,161)(110,160)(111,159)(112,158)(113,146)
(114,156)(115,155)(116,154)(117,153)(118,152)(119,151)(120,150)(121,149)
(122,148)(123,147);
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*s1*s2*s3*s1*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 >;
to this polytope