Polytope of Type {220,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {220,4}*1760
Also Known As : {220,4|2}. if this polytope has another name.
Group : SmallGroup(1760,991)
Rank : 3
Schlafli Type : {220,4}
Number of vertices, edges, etc : 220, 440, 4
Order of s₀s₁s₂ : 220
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {220,2}*880, {110,4}*880
   4-fold quotients : {110,2}*440
   5-fold quotients : {44,4}*352
   8-fold quotients : {55,2}*220
   10-fold quotients : {44,2}*176, {22,4}*176
   11-fold quotients : {20,4}*160
   20-fold quotients : {22,2}*88
   22-fold quotients : {20,2}*80, {10,4}*80
   40-fold quotients : {11,2}*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 := (  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 12, 45)( 13, 55)( 14, 54)
( 15, 53)( 16, 52)( 17, 51)( 18, 50)( 19, 49)( 20, 48)( 21, 47)( 22, 46)
( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)( 29, 39)( 30, 38)
( 31, 37)( 32, 36)( 33, 35)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)
( 67,100)( 68,110)( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)( 74,104)
( 75,103)( 76,102)( 77,101)( 78, 89)( 79, 99)( 80, 98)( 81, 97)( 82, 96)
( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)( 88, 90)(112,121)(113,120)
(114,119)(115,118)(116,117)(122,155)(123,165)(124,164)(125,163)(126,162)
(127,161)(128,160)(129,159)(130,158)(131,157)(132,156)(133,144)(134,154)
(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)(142,146)
(143,145)(167,176)(168,175)(169,174)(170,173)(171,172)(177,210)(178,220)
(179,219)(180,218)(181,217)(182,216)(183,215)(184,214)(185,213)(186,212)
(187,211)(188,199)(189,209)(190,208)(191,207)(192,206)(193,205)(194,204)
(195,203)(196,202)(197,201)(198,200)(221,276)(222,286)(223,285)(224,284)
(225,283)(226,282)(227,281)(228,280)(229,279)(230,278)(231,277)(232,320)
(233,330)(234,329)(235,328)(236,327)(237,326)(238,325)(239,324)(240,323)
(241,322)(242,321)(243,309)(244,319)(245,318)(246,317)(247,316)(248,315)
(249,314)(250,313)(251,312)(252,311)(253,310)(254,298)(255,308)(256,307)
(257,306)(258,305)(259,304)(260,303)(261,302)(262,301)(263,300)(264,299)
(265,287)(266,297)(267,296)(268,295)(269,294)(270,293)(271,292)(272,291)
(273,290)(274,289)(275,288)(331,386)(332,396)(333,395)(334,394)(335,393)
(336,392)(337,391)(338,390)(339,389)(340,388)(341,387)(342,430)(343,440)
(344,439)(345,438)(346,437)(347,436)(348,435)(349,434)(350,433)(351,432)
(352,431)(353,419)(354,429)(355,428)(356,427)(357,426)(358,425)(359,424)
(360,423)(361,422)(362,421)(363,420)(364,408)(365,418)(366,417)(367,416)
(368,415)(369,414)(370,413)(371,412)(372,411)(373,410)(374,409)(375,397)
(376,407)(377,406)(378,405)(379,404)(380,403)(381,402)(382,401)(383,400)
(384,399)(385,398);;
s1 := (  1,233)(  2,232)(  3,242)(  4,241)(  5,240)(  6,239)(  7,238)(  8,237)
(  9,236)( 10,235)( 11,234)( 12,222)( 13,221)( 14,231)( 15,230)( 16,229)
( 17,228)( 18,227)( 19,226)( 20,225)( 21,224)( 22,223)( 23,266)( 24,265)
( 25,275)( 26,274)( 27,273)( 28,272)( 29,271)( 30,270)( 31,269)( 32,268)
( 33,267)( 34,255)( 35,254)( 36,264)( 37,263)( 38,262)( 39,261)( 40,260)
( 41,259)( 42,258)( 43,257)( 44,256)( 45,244)( 46,243)( 47,253)( 48,252)
( 49,251)( 50,250)( 51,249)( 52,248)( 53,247)( 54,246)( 55,245)( 56,288)
( 57,287)( 58,297)( 59,296)( 60,295)( 61,294)( 62,293)( 63,292)( 64,291)
( 65,290)( 66,289)( 67,277)( 68,276)( 69,286)( 70,285)( 71,284)( 72,283)
( 73,282)( 74,281)( 75,280)( 76,279)( 77,278)( 78,321)( 79,320)( 80,330)
( 81,329)( 82,328)( 83,327)( 84,326)( 85,325)( 86,324)( 87,323)( 88,322)
( 89,310)( 90,309)( 91,319)( 92,318)( 93,317)( 94,316)( 95,315)( 96,314)
( 97,313)( 98,312)( 99,311)(100,299)(101,298)(102,308)(103,307)(104,306)
(105,305)(106,304)(107,303)(108,302)(109,301)(110,300)(111,343)(112,342)
(113,352)(114,351)(115,350)(116,349)(117,348)(118,347)(119,346)(120,345)
(121,344)(122,332)(123,331)(124,341)(125,340)(126,339)(127,338)(128,337)
(129,336)(130,335)(131,334)(132,333)(133,376)(134,375)(135,385)(136,384)
(137,383)(138,382)(139,381)(140,380)(141,379)(142,378)(143,377)(144,365)
(145,364)(146,374)(147,373)(148,372)(149,371)(150,370)(151,369)(152,368)
(153,367)(154,366)(155,354)(156,353)(157,363)(158,362)(159,361)(160,360)
(161,359)(162,358)(163,357)(164,356)(165,355)(166,398)(167,397)(168,407)
(169,406)(170,405)(171,404)(172,403)(173,402)(174,401)(175,400)(176,399)
(177,387)(178,386)(179,396)(180,395)(181,394)(182,393)(183,392)(184,391)
(185,390)(186,389)(187,388)(188,431)(189,430)(190,440)(191,439)(192,438)
(193,437)(194,436)(195,435)(196,434)(197,433)(198,432)(199,420)(200,419)
(201,429)(202,428)(203,427)(204,426)(205,425)(206,424)(207,423)(208,422)
(209,421)(210,409)(211,408)(212,418)(213,417)(214,416)(215,415)(216,414)
(217,413)(218,412)(219,411)(220,410);;
s2 := (221,331)(222,332)(223,333)(224,334)(225,335)(226,336)(227,337)(228,338)
(229,339)(230,340)(231,341)(232,342)(233,343)(234,344)(235,345)(236,346)
(237,347)(238,348)(239,349)(240,350)(241,351)(242,352)(243,353)(244,354)
(245,355)(246,356)(247,357)(248,358)(249,359)(250,360)(251,361)(252,362)
(253,363)(254,364)(255,365)(256,366)(257,367)(258,368)(259,369)(260,370)
(261,371)(262,372)(263,373)(264,374)(265,375)(266,376)(267,377)(268,378)
(269,379)(270,380)(271,381)(272,382)(273,383)(274,384)(275,385)(276,386)
(277,387)(278,388)(279,389)(280,390)(281,391)(282,392)(283,393)(284,394)
(285,395)(286,396)(287,397)(288,398)(289,399)(290,400)(291,401)(292,402)
(293,403)(294,404)(295,405)(296,406)(297,407)(298,408)(299,409)(300,410)
(301,411)(302,412)(303,413)(304,414)(305,415)(306,416)(307,417)(308,418)
(309,419)(310,420)(311,421)(312,422)(313,423)(314,424)(315,425)(316,426)
(317,427)(318,428)(319,429)(320,430)(321,431)(322,432)(323,433)(324,434)
(325,435)(326,436)(327,437)(328,438)(329,439)(330,440);;
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, 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*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*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*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*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)( 12, 45)( 13, 55)
( 14, 54)( 15, 53)( 16, 52)( 17, 51)( 18, 50)( 19, 49)( 20, 48)( 21, 47)
( 22, 46)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)( 29, 39)
( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 57, 66)( 58, 65)( 59, 64)( 60, 63)
( 61, 62)( 67,100)( 68,110)( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)
( 74,104)( 75,103)( 76,102)( 77,101)( 78, 89)( 79, 99)( 80, 98)( 81, 97)
( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)( 88, 90)(112,121)
(113,120)(114,119)(115,118)(116,117)(122,155)(123,165)(124,164)(125,163)
(126,162)(127,161)(128,160)(129,159)(130,158)(131,157)(132,156)(133,144)
(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)
(142,146)(143,145)(167,176)(168,175)(169,174)(170,173)(171,172)(177,210)
(178,220)(179,219)(180,218)(181,217)(182,216)(183,215)(184,214)(185,213)
(186,212)(187,211)(188,199)(189,209)(190,208)(191,207)(192,206)(193,205)
(194,204)(195,203)(196,202)(197,201)(198,200)(221,276)(222,286)(223,285)
(224,284)(225,283)(226,282)(227,281)(228,280)(229,279)(230,278)(231,277)
(232,320)(233,330)(234,329)(235,328)(236,327)(237,326)(238,325)(239,324)
(240,323)(241,322)(242,321)(243,309)(244,319)(245,318)(246,317)(247,316)
(248,315)(249,314)(250,313)(251,312)(252,311)(253,310)(254,298)(255,308)
(256,307)(257,306)(258,305)(259,304)(260,303)(261,302)(262,301)(263,300)
(264,299)(265,287)(266,297)(267,296)(268,295)(269,294)(270,293)(271,292)
(272,291)(273,290)(274,289)(275,288)(331,386)(332,396)(333,395)(334,394)
(335,393)(336,392)(337,391)(338,390)(339,389)(340,388)(341,387)(342,430)
(343,440)(344,439)(345,438)(346,437)(347,436)(348,435)(349,434)(350,433)
(351,432)(352,431)(353,419)(354,429)(355,428)(356,427)(357,426)(358,425)
(359,424)(360,423)(361,422)(362,421)(363,420)(364,408)(365,418)(366,417)
(367,416)(368,415)(369,414)(370,413)(371,412)(372,411)(373,410)(374,409)
(375,397)(376,407)(377,406)(378,405)(379,404)(380,403)(381,402)(382,401)
(383,400)(384,399)(385,398);
s1 := Sym(440)!(  1,233)(  2,232)(  3,242)(  4,241)(  5,240)(  6,239)(  7,238)
(  8,237)(  9,236)( 10,235)( 11,234)( 12,222)( 13,221)( 14,231)( 15,230)
( 16,229)( 17,228)( 18,227)( 19,226)( 20,225)( 21,224)( 22,223)( 23,266)
( 24,265)( 25,275)( 26,274)( 27,273)( 28,272)( 29,271)( 30,270)( 31,269)
( 32,268)( 33,267)( 34,255)( 35,254)( 36,264)( 37,263)( 38,262)( 39,261)
( 40,260)( 41,259)( 42,258)( 43,257)( 44,256)( 45,244)( 46,243)( 47,253)
( 48,252)( 49,251)( 50,250)( 51,249)( 52,248)( 53,247)( 54,246)( 55,245)
( 56,288)( 57,287)( 58,297)( 59,296)( 60,295)( 61,294)( 62,293)( 63,292)
( 64,291)( 65,290)( 66,289)( 67,277)( 68,276)( 69,286)( 70,285)( 71,284)
( 72,283)( 73,282)( 74,281)( 75,280)( 76,279)( 77,278)( 78,321)( 79,320)
( 80,330)( 81,329)( 82,328)( 83,327)( 84,326)( 85,325)( 86,324)( 87,323)
( 88,322)( 89,310)( 90,309)( 91,319)( 92,318)( 93,317)( 94,316)( 95,315)
( 96,314)( 97,313)( 98,312)( 99,311)(100,299)(101,298)(102,308)(103,307)
(104,306)(105,305)(106,304)(107,303)(108,302)(109,301)(110,300)(111,343)
(112,342)(113,352)(114,351)(115,350)(116,349)(117,348)(118,347)(119,346)
(120,345)(121,344)(122,332)(123,331)(124,341)(125,340)(126,339)(127,338)
(128,337)(129,336)(130,335)(131,334)(132,333)(133,376)(134,375)(135,385)
(136,384)(137,383)(138,382)(139,381)(140,380)(141,379)(142,378)(143,377)
(144,365)(145,364)(146,374)(147,373)(148,372)(149,371)(150,370)(151,369)
(152,368)(153,367)(154,366)(155,354)(156,353)(157,363)(158,362)(159,361)
(160,360)(161,359)(162,358)(163,357)(164,356)(165,355)(166,398)(167,397)
(168,407)(169,406)(170,405)(171,404)(172,403)(173,402)(174,401)(175,400)
(176,399)(177,387)(178,386)(179,396)(180,395)(181,394)(182,393)(183,392)
(184,391)(185,390)(186,389)(187,388)(188,431)(189,430)(190,440)(191,439)
(192,438)(193,437)(194,436)(195,435)(196,434)(197,433)(198,432)(199,420)
(200,419)(201,429)(202,428)(203,427)(204,426)(205,425)(206,424)(207,423)
(208,422)(209,421)(210,409)(211,408)(212,418)(213,417)(214,416)(215,415)
(216,414)(217,413)(218,412)(219,411)(220,410);
s2 := Sym(440)!(221,331)(222,332)(223,333)(224,334)(225,335)(226,336)(227,337)
(228,338)(229,339)(230,340)(231,341)(232,342)(233,343)(234,344)(235,345)
(236,346)(237,347)(238,348)(239,349)(240,350)(241,351)(242,352)(243,353)
(244,354)(245,355)(246,356)(247,357)(248,358)(249,359)(250,360)(251,361)
(252,362)(253,363)(254,364)(255,365)(256,366)(257,367)(258,368)(259,369)
(260,370)(261,371)(262,372)(263,373)(264,374)(265,375)(266,376)(267,377)
(268,378)(269,379)(270,380)(271,381)(272,382)(273,383)(274,384)(275,385)
(276,386)(277,387)(278,388)(279,389)(280,390)(281,391)(282,392)(283,393)
(284,394)(285,395)(286,396)(287,397)(288,398)(289,399)(290,400)(291,401)
(292,402)(293,403)(294,404)(295,405)(296,406)(297,407)(298,408)(299,409)
(300,410)(301,411)(302,412)(303,413)(304,414)(305,415)(306,416)(307,417)
(308,418)(309,419)(310,420)(311,421)(312,422)(313,423)(314,424)(315,425)
(316,426)(317,427)(318,428)(319,429)(320,430)(321,431)(322,432)(323,433)
(324,434)(325,435)(326,436)(327,437)(328,438)(329,439)(330,440);
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, 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*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*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*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*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