Polytope of Type {20,44}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,44}*1760
Also Known As : {20,44|2}. if this polytope has another name.
Group : SmallGroup(1760,702)
Rank : 3
Schlafli Type : {20,44}
Number of vertices, edges, etc : 20, 440, 44
Order of s0s1s2 : 220
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, {10,44}*880
4-fold quotients : {10,22}*440
5-fold quotients : {4,44}*352
10-fold quotients : {2,44}*176, {4,22}*176
11-fold quotients : {20,4}*160
20-fold quotients : {2,22}*88
22-fold quotients : {20,2}*80, {10,4}*80
40-fold quotients : {2,11}*44
44-fold quotients : {10,2}*40
55-fold quotients : {4,4}*32
88-fold quotients : {5,2}*20
110-fold quotients : {2,4}*16, {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)(122,155)(123,156)(124,157)(125,158)
(126,159)(127,160)(128,161)(129,162)(130,163)(131,164)(132,165)(133,144)
(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)(141,152)
(142,153)(143,154)(177,210)(178,211)(179,212)(180,213)(181,214)(182,215)
(183,216)(184,217)(185,218)(186,219)(187,220)(188,199)(189,200)(190,201)
(191,202)(192,203)(193,204)(194,205)(195,206)(196,207)(197,208)(198,209)
(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)(111,342)(112,352)
(113,351)(114,350)(115,349)(116,348)(117,347)(118,346)(119,345)(120,344)
(121,343)(122,331)(123,341)(124,340)(125,339)(126,338)(127,337)(128,336)
(129,335)(130,334)(131,333)(132,332)(133,375)(134,385)(135,384)(136,383)
(137,382)(138,381)(139,380)(140,379)(141,378)(142,377)(143,376)(144,364)
(145,374)(146,373)(147,372)(148,371)(149,370)(150,369)(151,368)(152,367)
(153,366)(154,365)(155,353)(156,363)(157,362)(158,361)(159,360)(160,359)
(161,358)(162,357)(163,356)(164,355)(165,354)(166,397)(167,407)(168,406)
(169,405)(170,404)(171,403)(172,402)(173,401)(174,400)(175,399)(176,398)
(177,386)(178,396)(179,395)(180,394)(181,393)(182,392)(183,391)(184,390)
(185,389)(186,388)(187,387)(188,430)(189,440)(190,439)(191,438)(192,437)
(193,436)(194,435)(195,434)(196,433)(197,432)(198,431)(199,419)(200,429)
(201,428)(202,427)(203,426)(204,425)(205,424)(206,423)(207,422)(208,421)
(209,420)(210,408)(211,418)(212,417)(213,416)(214,415)(215,414)(216,413)
(217,412)(218,411)(219,410)(220,409);;
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)(221,277)(222,276)(223,286)(224,285)
(225,284)(226,283)(227,282)(228,281)(229,280)(230,279)(231,278)(232,288)
(233,287)(234,297)(235,296)(236,295)(237,294)(238,293)(239,292)(240,291)
(241,290)(242,289)(243,299)(244,298)(245,308)(246,307)(247,306)(248,305)
(249,304)(250,303)(251,302)(252,301)(253,300)(254,310)(255,309)(256,319)
(257,318)(258,317)(259,316)(260,315)(261,314)(262,313)(263,312)(264,311)
(265,321)(266,320)(267,330)(268,329)(269,328)(270,327)(271,326)(272,325)
(273,324)(274,323)(275,322)(331,387)(332,386)(333,396)(334,395)(335,394)
(336,393)(337,392)(338,391)(339,390)(340,389)(341,388)(342,398)(343,397)
(344,407)(345,406)(346,405)(347,404)(348,403)(349,402)(350,401)(351,400)
(352,399)(353,409)(354,408)(355,418)(356,417)(357,416)(358,415)(359,414)
(360,413)(361,412)(362,411)(363,410)(364,420)(365,419)(366,429)(367,428)
(368,427)(369,426)(370,425)(371,424)(372,423)(373,422)(374,421)(375,431)
(376,430)(377,440)(378,439)(379,438)(380,437)(381,436)(382,435)(383,434)
(384,433)(385,432);;
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,
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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)(122,155)(123,156)(124,157)
(125,158)(126,159)(127,160)(128,161)(129,162)(130,163)(131,164)(132,165)
(133,144)(134,145)(135,146)(136,147)(137,148)(138,149)(139,150)(140,151)
(141,152)(142,153)(143,154)(177,210)(178,211)(179,212)(180,213)(181,214)
(182,215)(183,216)(184,217)(185,218)(186,219)(187,220)(188,199)(189,200)
(190,201)(191,202)(192,203)(193,204)(194,205)(195,206)(196,207)(197,208)
(198,209)(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)(111,342)
(112,352)(113,351)(114,350)(115,349)(116,348)(117,347)(118,346)(119,345)
(120,344)(121,343)(122,331)(123,341)(124,340)(125,339)(126,338)(127,337)
(128,336)(129,335)(130,334)(131,333)(132,332)(133,375)(134,385)(135,384)
(136,383)(137,382)(138,381)(139,380)(140,379)(141,378)(142,377)(143,376)
(144,364)(145,374)(146,373)(147,372)(148,371)(149,370)(150,369)(151,368)
(152,367)(153,366)(154,365)(155,353)(156,363)(157,362)(158,361)(159,360)
(160,359)(161,358)(162,357)(163,356)(164,355)(165,354)(166,397)(167,407)
(168,406)(169,405)(170,404)(171,403)(172,402)(173,401)(174,400)(175,399)
(176,398)(177,386)(178,396)(179,395)(180,394)(181,393)(182,392)(183,391)
(184,390)(185,389)(186,388)(187,387)(188,430)(189,440)(190,439)(191,438)
(192,437)(193,436)(194,435)(195,434)(196,433)(197,432)(198,431)(199,419)
(200,429)(201,428)(202,427)(203,426)(204,425)(205,424)(206,423)(207,422)
(208,421)(209,420)(210,408)(211,418)(212,417)(213,416)(214,415)(215,414)
(216,413)(217,412)(218,411)(219,410)(220,409);
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)(221,277)(222,276)(223,286)
(224,285)(225,284)(226,283)(227,282)(228,281)(229,280)(230,279)(231,278)
(232,288)(233,287)(234,297)(235,296)(236,295)(237,294)(238,293)(239,292)
(240,291)(241,290)(242,289)(243,299)(244,298)(245,308)(246,307)(247,306)
(248,305)(249,304)(250,303)(251,302)(252,301)(253,300)(254,310)(255,309)
(256,319)(257,318)(258,317)(259,316)(260,315)(261,314)(262,313)(263,312)
(264,311)(265,321)(266,320)(267,330)(268,329)(269,328)(270,327)(271,326)
(272,325)(273,324)(274,323)(275,322)(331,387)(332,386)(333,396)(334,395)
(335,394)(336,393)(337,392)(338,391)(339,390)(340,389)(341,388)(342,398)
(343,397)(344,407)(345,406)(346,405)(347,404)(348,403)(349,402)(350,401)
(351,400)(352,399)(353,409)(354,408)(355,418)(356,417)(357,416)(358,415)
(359,414)(360,413)(361,412)(362,411)(363,410)(364,420)(365,419)(366,429)
(367,428)(368,427)(369,426)(370,425)(371,424)(372,423)(373,422)(374,421)
(375,431)(376,430)(377,440)(378,439)(379,438)(380,437)(381,436)(382,435)
(383,434)(384,433)(385,432);
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,
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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope