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