Polytope of Type {44,18}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,18}*1584a
Also Known As : {44,18|2}. if this polytope has another name.
Group : SmallGroup(1584,114)
Rank : 3
Schlafli Type : {44,18}
Number of vertices, edges, etc : 44, 396, 18
Order of s₀s₁s₂ : 396
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 : {22,18}*792
   3-fold quotients : {44,6}*528a
   6-fold quotients : {22,6}*264
   9-fold quotients : {44,2}*176
   11-fold quotients : {4,18}*144a
   18-fold quotients : {22,2}*88
   22-fold quotients : {2,18}*72
   33-fold quotients : {4,6}*48a
   36-fold quotients : {11,2}*44
   44-fold quotients : {2,9}*36
   66-fold quotients : {2,6}*24
   99-fold quotients : {4,2}*16
   132-fold quotients : {2,3}*12
   198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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