Polytope of Type {22,40}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,40}*1760
Also Known As : {22,40|2}. if this polytope has another name.
Group : SmallGroup(1760,474)
Rank : 3
Schlafli Type : {22,40}
Number of vertices, edges, etc : 22, 440, 40
Order of s0s1s2 : 440
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {22,20}*880
4-fold quotients : {22,10}*440
5-fold quotients : {22,8}*352
10-fold quotients : {22,4}*176
11-fold quotients : {2,40}*160
20-fold quotients : {22,2}*88
22-fold quotients : {2,20}*80
40-fold quotients : {11,2}*44
44-fold quotients : {2,10}*40
55-fold quotients : {2,8}*32
88-fold quotients : {2,5}*20
110-fold quotients : {2,4}*16
220-fold quotients : {2,2}*8
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)(244,253)(245,252)
(246,251)(247,250)(248,249)(255,264)(256,263)(257,262)(258,261)(259,260)
(266,275)(267,274)(268,273)(269,272)(270,271)(277,286)(278,285)(279,284)
(280,283)(281,282)(288,297)(289,296)(290,295)(291,294)(292,293)(299,308)
(300,307)(301,306)(302,305)(303,304)(310,319)(311,318)(312,317)(313,316)
(314,315)(321,330)(322,329)(323,328)(324,327)(325,326)(332,341)(333,340)
(334,339)(335,338)(336,337)(343,352)(344,351)(345,350)(346,349)(347,348)
(354,363)(355,362)(356,361)(357,360)(358,359)(365,374)(366,373)(367,372)
(368,371)(369,370)(376,385)(377,384)(378,383)(379,382)(380,381)(387,396)
(388,395)(389,394)(390,393)(391,392)(398,407)(399,406)(400,405)(401,404)
(402,403)(409,418)(410,417)(411,416)(412,415)(413,414)(420,429)(421,428)
(422,427)(423,426)(424,425)(431,440)(432,439)(433,438)(434,437)(435,436);;
s1 := ( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 46)( 13, 45)( 14, 55)
( 15, 54)( 16, 53)( 17, 52)( 18, 51)( 19, 50)( 20, 49)( 21, 48)( 22, 47)
( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)( 30, 39)
( 31, 38)( 32, 37)( 33, 36)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)
( 67,101)( 68,100)( 69,110)( 70,109)( 71,108)( 72,107)( 73,106)( 74,105)
( 75,104)( 76,103)( 77,102)( 78, 90)( 79, 89)( 80, 99)( 81, 98)( 82, 97)
( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)( 88, 91)(111,167)(112,166)
(113,176)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,169)
(121,168)(122,211)(123,210)(124,220)(125,219)(126,218)(127,217)(128,216)
(129,215)(130,214)(131,213)(132,212)(133,200)(134,199)(135,209)(136,208)
(137,207)(138,206)(139,205)(140,204)(141,203)(142,202)(143,201)(144,189)
(145,188)(146,198)(147,197)(148,196)(149,195)(150,194)(151,193)(152,192)
(153,191)(154,190)(155,178)(156,177)(157,187)(158,186)(159,185)(160,184)
(161,183)(162,182)(163,181)(164,180)(165,179)(221,332)(222,331)(223,341)
(224,340)(225,339)(226,338)(227,337)(228,336)(229,335)(230,334)(231,333)
(232,376)(233,375)(234,385)(235,384)(236,383)(237,382)(238,381)(239,380)
(240,379)(241,378)(242,377)(243,365)(244,364)(245,374)(246,373)(247,372)
(248,371)(249,370)(250,369)(251,368)(252,367)(253,366)(254,354)(255,353)
(256,363)(257,362)(258,361)(259,360)(260,359)(261,358)(262,357)(263,356)
(264,355)(265,343)(266,342)(267,352)(268,351)(269,350)(270,349)(271,348)
(272,347)(273,346)(274,345)(275,344)(276,387)(277,386)(278,396)(279,395)
(280,394)(281,393)(282,392)(283,391)(284,390)(285,389)(286,388)(287,431)
(288,430)(289,440)(290,439)(291,438)(292,437)(293,436)(294,435)(295,434)
(296,433)(297,432)(298,420)(299,419)(300,429)(301,428)(302,427)(303,426)
(304,425)(305,424)(306,423)(307,422)(308,421)(309,409)(310,408)(311,418)
(312,417)(313,416)(314,415)(315,414)(316,413)(317,412)(318,411)(319,410)
(320,398)(321,397)(322,407)(323,406)(324,405)(325,404)(326,403)(327,402)
(328,401)(329,400)(330,399);;
s2 := ( 1,232)( 2,233)( 3,234)( 4,235)( 5,236)( 6,237)( 7,238)( 8,239)
( 9,240)( 10,241)( 11,242)( 12,221)( 13,222)( 14,223)( 15,224)( 16,225)
( 17,226)( 18,227)( 19,228)( 20,229)( 21,230)( 22,231)( 23,265)( 24,266)
( 25,267)( 26,268)( 27,269)( 28,270)( 29,271)( 30,272)( 31,273)( 32,274)
( 33,275)( 34,254)( 35,255)( 36,256)( 37,257)( 38,258)( 39,259)( 40,260)
( 41,261)( 42,262)( 43,263)( 44,264)( 45,243)( 46,244)( 47,245)( 48,246)
( 49,247)( 50,248)( 51,249)( 52,250)( 53,251)( 54,252)( 55,253)( 56,287)
( 57,288)( 58,289)( 59,290)( 60,291)( 61,292)( 62,293)( 63,294)( 64,295)
( 65,296)( 66,297)( 67,276)( 68,277)( 69,278)( 70,279)( 71,280)( 72,281)
( 73,282)( 74,283)( 75,284)( 76,285)( 77,286)( 78,320)( 79,321)( 80,322)
( 81,323)( 82,324)( 83,325)( 84,326)( 85,327)( 86,328)( 87,329)( 88,330)
( 89,309)( 90,310)( 91,311)( 92,312)( 93,313)( 94,314)( 95,315)( 96,316)
( 97,317)( 98,318)( 99,319)(100,298)(101,299)(102,300)(103,301)(104,302)
(105,303)(106,304)(107,305)(108,306)(109,307)(110,308)(111,397)(112,398)
(113,399)(114,400)(115,401)(116,402)(117,403)(118,404)(119,405)(120,406)
(121,407)(122,386)(123,387)(124,388)(125,389)(126,390)(127,391)(128,392)
(129,393)(130,394)(131,395)(132,396)(133,430)(134,431)(135,432)(136,433)
(137,434)(138,435)(139,436)(140,437)(141,438)(142,439)(143,440)(144,419)
(145,420)(146,421)(147,422)(148,423)(149,424)(150,425)(151,426)(152,427)
(153,428)(154,429)(155,408)(156,409)(157,410)(158,411)(159,412)(160,413)
(161,414)(162,415)(163,416)(164,417)(165,418)(166,342)(167,343)(168,344)
(169,345)(170,346)(171,347)(172,348)(173,349)(174,350)(175,351)(176,352)
(177,331)(178,332)(179,333)(180,334)(181,335)(182,336)(183,337)(184,338)
(185,339)(186,340)(187,341)(188,375)(189,376)(190,377)(191,378)(192,379)
(193,380)(194,381)(195,382)(196,383)(197,384)(198,385)(199,364)(200,365)
(201,366)(202,367)(203,368)(204,369)(205,370)(206,371)(207,372)(208,373)
(209,374)(210,353)(211,354)(212,355)(213,356)(214,357)(215,358)(216,359)
(217,360)(218,361)(219,362)(220,363);;
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*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(440)!( 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)(244,253)
(245,252)(246,251)(247,250)(248,249)(255,264)(256,263)(257,262)(258,261)
(259,260)(266,275)(267,274)(268,273)(269,272)(270,271)(277,286)(278,285)
(279,284)(280,283)(281,282)(288,297)(289,296)(290,295)(291,294)(292,293)
(299,308)(300,307)(301,306)(302,305)(303,304)(310,319)(311,318)(312,317)
(313,316)(314,315)(321,330)(322,329)(323,328)(324,327)(325,326)(332,341)
(333,340)(334,339)(335,338)(336,337)(343,352)(344,351)(345,350)(346,349)
(347,348)(354,363)(355,362)(356,361)(357,360)(358,359)(365,374)(366,373)
(367,372)(368,371)(369,370)(376,385)(377,384)(378,383)(379,382)(380,381)
(387,396)(388,395)(389,394)(390,393)(391,392)(398,407)(399,406)(400,405)
(401,404)(402,403)(409,418)(410,417)(411,416)(412,415)(413,414)(420,429)
(421,428)(422,427)(423,426)(424,425)(431,440)(432,439)(433,438)(434,437)
(435,436);
s1 := Sym(440)!( 1, 2)( 3, 11)( 4, 10)( 5, 9)( 6, 8)( 12, 46)( 13, 45)
( 14, 55)( 15, 54)( 16, 53)( 17, 52)( 18, 51)( 19, 50)( 20, 49)( 21, 48)
( 22, 47)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)( 29, 40)
( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 56, 57)( 58, 66)( 59, 65)( 60, 64)
( 61, 63)( 67,101)( 68,100)( 69,110)( 70,109)( 71,108)( 72,107)( 73,106)
( 74,105)( 75,104)( 76,103)( 77,102)( 78, 90)( 79, 89)( 80, 99)( 81, 98)
( 82, 97)( 83, 96)( 84, 95)( 85, 94)( 86, 93)( 87, 92)( 88, 91)(111,167)
(112,166)(113,176)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)
(120,169)(121,168)(122,211)(123,210)(124,220)(125,219)(126,218)(127,217)
(128,216)(129,215)(130,214)(131,213)(132,212)(133,200)(134,199)(135,209)
(136,208)(137,207)(138,206)(139,205)(140,204)(141,203)(142,202)(143,201)
(144,189)(145,188)(146,198)(147,197)(148,196)(149,195)(150,194)(151,193)
(152,192)(153,191)(154,190)(155,178)(156,177)(157,187)(158,186)(159,185)
(160,184)(161,183)(162,182)(163,181)(164,180)(165,179)(221,332)(222,331)
(223,341)(224,340)(225,339)(226,338)(227,337)(228,336)(229,335)(230,334)
(231,333)(232,376)(233,375)(234,385)(235,384)(236,383)(237,382)(238,381)
(239,380)(240,379)(241,378)(242,377)(243,365)(244,364)(245,374)(246,373)
(247,372)(248,371)(249,370)(250,369)(251,368)(252,367)(253,366)(254,354)
(255,353)(256,363)(257,362)(258,361)(259,360)(260,359)(261,358)(262,357)
(263,356)(264,355)(265,343)(266,342)(267,352)(268,351)(269,350)(270,349)
(271,348)(272,347)(273,346)(274,345)(275,344)(276,387)(277,386)(278,396)
(279,395)(280,394)(281,393)(282,392)(283,391)(284,390)(285,389)(286,388)
(287,431)(288,430)(289,440)(290,439)(291,438)(292,437)(293,436)(294,435)
(295,434)(296,433)(297,432)(298,420)(299,419)(300,429)(301,428)(302,427)
(303,426)(304,425)(305,424)(306,423)(307,422)(308,421)(309,409)(310,408)
(311,418)(312,417)(313,416)(314,415)(315,414)(316,413)(317,412)(318,411)
(319,410)(320,398)(321,397)(322,407)(323,406)(324,405)(325,404)(326,403)
(327,402)(328,401)(329,400)(330,399);
s2 := Sym(440)!( 1,232)( 2,233)( 3,234)( 4,235)( 5,236)( 6,237)( 7,238)
( 8,239)( 9,240)( 10,241)( 11,242)( 12,221)( 13,222)( 14,223)( 15,224)
( 16,225)( 17,226)( 18,227)( 19,228)( 20,229)( 21,230)( 22,231)( 23,265)
( 24,266)( 25,267)( 26,268)( 27,269)( 28,270)( 29,271)( 30,272)( 31,273)
( 32,274)( 33,275)( 34,254)( 35,255)( 36,256)( 37,257)( 38,258)( 39,259)
( 40,260)( 41,261)( 42,262)( 43,263)( 44,264)( 45,243)( 46,244)( 47,245)
( 48,246)( 49,247)( 50,248)( 51,249)( 52,250)( 53,251)( 54,252)( 55,253)
( 56,287)( 57,288)( 58,289)( 59,290)( 60,291)( 61,292)( 62,293)( 63,294)
( 64,295)( 65,296)( 66,297)( 67,276)( 68,277)( 69,278)( 70,279)( 71,280)
( 72,281)( 73,282)( 74,283)( 75,284)( 76,285)( 77,286)( 78,320)( 79,321)
( 80,322)( 81,323)( 82,324)( 83,325)( 84,326)( 85,327)( 86,328)( 87,329)
( 88,330)( 89,309)( 90,310)( 91,311)( 92,312)( 93,313)( 94,314)( 95,315)
( 96,316)( 97,317)( 98,318)( 99,319)(100,298)(101,299)(102,300)(103,301)
(104,302)(105,303)(106,304)(107,305)(108,306)(109,307)(110,308)(111,397)
(112,398)(113,399)(114,400)(115,401)(116,402)(117,403)(118,404)(119,405)
(120,406)(121,407)(122,386)(123,387)(124,388)(125,389)(126,390)(127,391)
(128,392)(129,393)(130,394)(131,395)(132,396)(133,430)(134,431)(135,432)
(136,433)(137,434)(138,435)(139,436)(140,437)(141,438)(142,439)(143,440)
(144,419)(145,420)(146,421)(147,422)(148,423)(149,424)(150,425)(151,426)
(152,427)(153,428)(154,429)(155,408)(156,409)(157,410)(158,411)(159,412)
(160,413)(161,414)(162,415)(163,416)(164,417)(165,418)(166,342)(167,343)
(168,344)(169,345)(170,346)(171,347)(172,348)(173,349)(174,350)(175,351)
(176,352)(177,331)(178,332)(179,333)(180,334)(181,335)(182,336)(183,337)
(184,338)(185,339)(186,340)(187,341)(188,375)(189,376)(190,377)(191,378)
(192,379)(193,380)(194,381)(195,382)(196,383)(197,384)(198,385)(199,364)
(200,365)(201,366)(202,367)(203,368)(204,369)(205,370)(206,371)(207,372)
(208,373)(209,374)(210,353)(211,354)(212,355)(213,356)(214,357)(215,358)
(216,359)(217,360)(218,361)(219,362)(220,363);
poly := sub<Sym(440)|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*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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