Polytope of Type {44,20}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,20}*1760
Also Known As : {44,20|2}. if this polytope has another name.
Group : SmallGroup(1760,702)
Rank : 3
Schlafli Type : {44,20}
Number of vertices, edges, etc : 44, 440, 20
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 : {22,20}*880, {44,10}*880
4-fold quotients : {22,10}*440
5-fold quotients : {44,4}*352
10-fold quotients : {44,2}*176, {22,4}*176
11-fold quotients : {4,20}*160
20-fold quotients : {22,2}*88
22-fold quotients : {2,20}*80, {4,10}*80
40-fold quotients : {11,2}*44
44-fold quotients : {2,10}*40
55-fold quotients : {4,4}*32
88-fold quotients : {2,5}*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 := ( 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)(221,276)(222,286)(223,285)(224,284)
(225,283)(226,282)(227,281)(228,280)(229,279)(230,278)(231,277)(232,287)
(233,297)(234,296)(235,295)(236,294)(237,293)(238,292)(239,291)(240,290)
(241,289)(242,288)(243,298)(244,308)(245,307)(246,306)(247,305)(248,304)
(249,303)(250,302)(251,301)(252,300)(253,299)(254,309)(255,319)(256,318)
(257,317)(258,316)(259,315)(260,314)(261,313)(262,312)(263,311)(264,310)
(265,320)(266,330)(267,329)(268,328)(269,327)(270,326)(271,325)(272,324)
(273,323)(274,322)(275,321)(331,386)(332,396)(333,395)(334,394)(335,393)
(336,392)(337,391)(338,390)(339,389)(340,388)(341,387)(342,397)(343,407)
(344,406)(345,405)(346,404)(347,403)(348,402)(349,401)(350,400)(351,399)
(352,398)(353,408)(354,418)(355,417)(356,416)(357,415)(358,414)(359,413)
(360,412)(361,411)(362,410)(363,409)(364,419)(365,429)(366,428)(367,427)
(368,426)(369,425)(370,424)(371,423)(372,422)(373,421)(374,420)(375,430)
(376,440)(377,439)(378,438)(379,437)(380,436)(381,435)(382,434)(383,433)
(384,432)(385,431);;
s1 := ( 1,222)( 2,221)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)( 8,226)
( 9,225)( 10,224)( 11,223)( 12,266)( 13,265)( 14,275)( 15,274)( 16,273)
( 17,272)( 18,271)( 19,270)( 20,269)( 21,268)( 22,267)( 23,255)( 24,254)
( 25,264)( 26,263)( 27,262)( 28,261)( 29,260)( 30,259)( 31,258)( 32,257)
( 33,256)( 34,244)( 35,243)( 36,253)( 37,252)( 38,251)( 39,250)( 40,249)
( 41,248)( 42,247)( 43,246)( 44,245)( 45,233)( 46,232)( 47,242)( 48,241)
( 49,240)( 50,239)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)( 56,277)
( 57,276)( 58,286)( 59,285)( 60,284)( 61,283)( 62,282)( 63,281)( 64,280)
( 65,279)( 66,278)( 67,321)( 68,320)( 69,330)( 70,329)( 71,328)( 72,327)
( 73,326)( 74,325)( 75,324)( 76,323)( 77,322)( 78,310)( 79,309)( 80,319)
( 81,318)( 82,317)( 83,316)( 84,315)( 85,314)( 86,313)( 87,312)( 88,311)
( 89,299)( 90,298)( 91,308)( 92,307)( 93,306)( 94,305)( 95,304)( 96,303)
( 97,302)( 98,301)( 99,300)(100,288)(101,287)(102,297)(103,296)(104,295)
(105,294)(106,293)(107,292)(108,291)(109,290)(110,289)(111,332)(112,331)
(113,341)(114,340)(115,339)(116,338)(117,337)(118,336)(119,335)(120,334)
(121,333)(122,376)(123,375)(124,385)(125,384)(126,383)(127,382)(128,381)
(129,380)(130,379)(131,378)(132,377)(133,365)(134,364)(135,374)(136,373)
(137,372)(138,371)(139,370)(140,369)(141,368)(142,367)(143,366)(144,354)
(145,353)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)(152,357)
(153,356)(154,355)(155,343)(156,342)(157,352)(158,351)(159,350)(160,349)
(161,348)(162,347)(163,346)(164,345)(165,344)(166,387)(167,386)(168,396)
(169,395)(170,394)(171,393)(172,392)(173,391)(174,390)(175,389)(176,388)
(177,431)(178,430)(179,440)(180,439)(181,438)(182,437)(183,436)(184,435)
(185,434)(186,433)(187,432)(188,420)(189,419)(190,429)(191,428)(192,427)
(193,426)(194,425)(195,424)(196,423)(197,422)(198,421)(199,409)(200,408)
(201,418)(202,417)(203,416)(204,415)(205,414)(206,413)(207,412)(208,411)
(209,410)(210,398)(211,397)(212,407)(213,406)(214,405)(215,404)(216,403)
(217,402)(218,401)(219,400)(220,399);;
s2 := ( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 16)( 6, 17)( 7, 18)( 8, 19)
( 9, 20)( 10, 21)( 11, 22)( 23, 45)( 24, 46)( 25, 47)( 26, 48)( 27, 49)
( 28, 50)( 29, 51)( 30, 52)( 31, 53)( 32, 54)( 33, 55)( 56, 67)( 57, 68)
( 58, 69)( 59, 70)( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)( 65, 76)
( 66, 77)( 78,100)( 79,101)( 80,102)( 81,103)( 82,104)( 83,105)( 84,106)
( 85,107)( 86,108)( 87,109)( 88,110)(111,122)(112,123)(113,124)(114,125)
(115,126)(116,127)(117,128)(118,129)(119,130)(120,131)(121,132)(133,155)
(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)(141,163)
(142,164)(143,165)(166,177)(167,178)(168,179)(169,180)(170,181)(171,182)
(172,183)(173,184)(174,185)(175,186)(176,187)(188,210)(189,211)(190,212)
(191,213)(192,214)(193,215)(194,216)(195,217)(196,218)(197,219)(198,220)
(221,342)(222,343)(223,344)(224,345)(225,346)(226,347)(227,348)(228,349)
(229,350)(230,351)(231,352)(232,331)(233,332)(234,333)(235,334)(236,335)
(237,336)(238,337)(239,338)(240,339)(241,340)(242,341)(243,375)(244,376)
(245,377)(246,378)(247,379)(248,380)(249,381)(250,382)(251,383)(252,384)
(253,385)(254,364)(255,365)(256,366)(257,367)(258,368)(259,369)(260,370)
(261,371)(262,372)(263,373)(264,374)(265,353)(266,354)(267,355)(268,356)
(269,357)(270,358)(271,359)(272,360)(273,361)(274,362)(275,363)(276,397)
(277,398)(278,399)(279,400)(280,401)(281,402)(282,403)(283,404)(284,405)
(285,406)(286,407)(287,386)(288,387)(289,388)(290,389)(291,390)(292,391)
(293,392)(294,393)(295,394)(296,395)(297,396)(298,430)(299,431)(300,432)
(301,433)(302,434)(303,435)(304,436)(305,437)(306,438)(307,439)(308,440)
(309,419)(310,420)(311,421)(312,422)(313,423)(314,424)(315,425)(316,426)
(317,427)(318,428)(319,429)(320,408)(321,409)(322,410)(323,411)(324,412)
(325,413)(326,414)(327,415)(328,416)(329,417)(330,418);;
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,
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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
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)(221,276)(222,286)(223,285)
(224,284)(225,283)(226,282)(227,281)(228,280)(229,279)(230,278)(231,277)
(232,287)(233,297)(234,296)(235,295)(236,294)(237,293)(238,292)(239,291)
(240,290)(241,289)(242,288)(243,298)(244,308)(245,307)(246,306)(247,305)
(248,304)(249,303)(250,302)(251,301)(252,300)(253,299)(254,309)(255,319)
(256,318)(257,317)(258,316)(259,315)(260,314)(261,313)(262,312)(263,311)
(264,310)(265,320)(266,330)(267,329)(268,328)(269,327)(270,326)(271,325)
(272,324)(273,323)(274,322)(275,321)(331,386)(332,396)(333,395)(334,394)
(335,393)(336,392)(337,391)(338,390)(339,389)(340,388)(341,387)(342,397)
(343,407)(344,406)(345,405)(346,404)(347,403)(348,402)(349,401)(350,400)
(351,399)(352,398)(353,408)(354,418)(355,417)(356,416)(357,415)(358,414)
(359,413)(360,412)(361,411)(362,410)(363,409)(364,419)(365,429)(366,428)
(367,427)(368,426)(369,425)(370,424)(371,423)(372,422)(373,421)(374,420)
(375,430)(376,440)(377,439)(378,438)(379,437)(380,436)(381,435)(382,434)
(383,433)(384,432)(385,431);
s1 := Sym(440)!( 1,222)( 2,221)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)
( 8,226)( 9,225)( 10,224)( 11,223)( 12,266)( 13,265)( 14,275)( 15,274)
( 16,273)( 17,272)( 18,271)( 19,270)( 20,269)( 21,268)( 22,267)( 23,255)
( 24,254)( 25,264)( 26,263)( 27,262)( 28,261)( 29,260)( 30,259)( 31,258)
( 32,257)( 33,256)( 34,244)( 35,243)( 36,253)( 37,252)( 38,251)( 39,250)
( 40,249)( 41,248)( 42,247)( 43,246)( 44,245)( 45,233)( 46,232)( 47,242)
( 48,241)( 49,240)( 50,239)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)
( 56,277)( 57,276)( 58,286)( 59,285)( 60,284)( 61,283)( 62,282)( 63,281)
( 64,280)( 65,279)( 66,278)( 67,321)( 68,320)( 69,330)( 70,329)( 71,328)
( 72,327)( 73,326)( 74,325)( 75,324)( 76,323)( 77,322)( 78,310)( 79,309)
( 80,319)( 81,318)( 82,317)( 83,316)( 84,315)( 85,314)( 86,313)( 87,312)
( 88,311)( 89,299)( 90,298)( 91,308)( 92,307)( 93,306)( 94,305)( 95,304)
( 96,303)( 97,302)( 98,301)( 99,300)(100,288)(101,287)(102,297)(103,296)
(104,295)(105,294)(106,293)(107,292)(108,291)(109,290)(110,289)(111,332)
(112,331)(113,341)(114,340)(115,339)(116,338)(117,337)(118,336)(119,335)
(120,334)(121,333)(122,376)(123,375)(124,385)(125,384)(126,383)(127,382)
(128,381)(129,380)(130,379)(131,378)(132,377)(133,365)(134,364)(135,374)
(136,373)(137,372)(138,371)(139,370)(140,369)(141,368)(142,367)(143,366)
(144,354)(145,353)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)
(152,357)(153,356)(154,355)(155,343)(156,342)(157,352)(158,351)(159,350)
(160,349)(161,348)(162,347)(163,346)(164,345)(165,344)(166,387)(167,386)
(168,396)(169,395)(170,394)(171,393)(172,392)(173,391)(174,390)(175,389)
(176,388)(177,431)(178,430)(179,440)(180,439)(181,438)(182,437)(183,436)
(184,435)(185,434)(186,433)(187,432)(188,420)(189,419)(190,429)(191,428)
(192,427)(193,426)(194,425)(195,424)(196,423)(197,422)(198,421)(199,409)
(200,408)(201,418)(202,417)(203,416)(204,415)(205,414)(206,413)(207,412)
(208,411)(209,410)(210,398)(211,397)(212,407)(213,406)(214,405)(215,404)
(216,403)(217,402)(218,401)(219,400)(220,399);
s2 := Sym(440)!( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 16)( 6, 17)( 7, 18)
( 8, 19)( 9, 20)( 10, 21)( 11, 22)( 23, 45)( 24, 46)( 25, 47)( 26, 48)
( 27, 49)( 28, 50)( 29, 51)( 30, 52)( 31, 53)( 32, 54)( 33, 55)( 56, 67)
( 57, 68)( 58, 69)( 59, 70)( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)
( 65, 76)( 66, 77)( 78,100)( 79,101)( 80,102)( 81,103)( 82,104)( 83,105)
( 84,106)( 85,107)( 86,108)( 87,109)( 88,110)(111,122)(112,123)(113,124)
(114,125)(115,126)(116,127)(117,128)(118,129)(119,130)(120,131)(121,132)
(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)
(141,163)(142,164)(143,165)(166,177)(167,178)(168,179)(169,180)(170,181)
(171,182)(172,183)(173,184)(174,185)(175,186)(176,187)(188,210)(189,211)
(190,212)(191,213)(192,214)(193,215)(194,216)(195,217)(196,218)(197,219)
(198,220)(221,342)(222,343)(223,344)(224,345)(225,346)(226,347)(227,348)
(228,349)(229,350)(230,351)(231,352)(232,331)(233,332)(234,333)(235,334)
(236,335)(237,336)(238,337)(239,338)(240,339)(241,340)(242,341)(243,375)
(244,376)(245,377)(246,378)(247,379)(248,380)(249,381)(250,382)(251,383)
(252,384)(253,385)(254,364)(255,365)(256,366)(257,367)(258,368)(259,369)
(260,370)(261,371)(262,372)(263,373)(264,374)(265,353)(266,354)(267,355)
(268,356)(269,357)(270,358)(271,359)(272,360)(273,361)(274,362)(275,363)
(276,397)(277,398)(278,399)(279,400)(280,401)(281,402)(282,403)(283,404)
(284,405)(285,406)(286,407)(287,386)(288,387)(289,388)(290,389)(291,390)
(292,391)(293,392)(294,393)(295,394)(296,395)(297,396)(298,430)(299,431)
(300,432)(301,433)(302,434)(303,435)(304,436)(305,437)(306,438)(307,439)
(308,440)(309,419)(310,420)(311,421)(312,422)(313,423)(314,424)(315,425)
(316,426)(317,427)(318,428)(319,429)(320,408)(321,409)(322,410)(323,411)
(324,412)(325,413)(326,414)(327,415)(328,416)(329,417)(330,418);
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,
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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope