Polytope of Type {44,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {44,18}*1584b
if this polytope has a name.
Group : SmallGroup(1584,364)
Rank : 3
Schlafli Type : {44,18}
Number of vertices, edges, etc : 44, 396, 18
Order of s0s1s2 : 99
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-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) :
3-fold quotients : {44,6}*528b
11-fold quotients : {4,18}*144c
22-fold quotients : {4,9}*72
33-fold quotients : {4,6}*48b
66-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13,123)( 14,124)
( 15,121)( 16,122)( 17,127)( 18,128)( 19,125)( 20,126)( 21,131)( 22,132)
( 23,129)( 24,130)( 25,111)( 26,112)( 27,109)( 28,110)( 29,115)( 30,116)
( 31,113)( 32,114)( 33,119)( 34,120)( 35,117)( 36,118)( 37, 99)( 38,100)
( 39, 97)( 40, 98)( 41,103)( 42,104)( 43,101)( 44,102)( 45,107)( 46,108)
( 47,105)( 48,106)( 49, 87)( 50, 88)( 51, 85)( 52, 86)( 53, 91)( 54, 92)
( 55, 89)( 56, 90)( 57, 95)( 58, 96)( 59, 93)( 60, 94)( 61, 75)( 62, 76)
( 63, 73)( 64, 74)( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 83)( 70, 84)
( 71, 81)( 72, 82)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,255)(146,256)(147,253)(148,254)(149,259)(150,260)(151,257)(152,258)
(153,263)(154,264)(155,261)(156,262)(157,243)(158,244)(159,241)(160,242)
(161,247)(162,248)(163,245)(164,246)(165,251)(166,252)(167,249)(168,250)
(169,231)(170,232)(171,229)(172,230)(173,235)(174,236)(175,233)(176,234)
(177,239)(178,240)(179,237)(180,238)(181,219)(182,220)(183,217)(184,218)
(185,223)(186,224)(187,221)(188,222)(189,227)(190,228)(191,225)(192,226)
(193,207)(194,208)(195,205)(196,206)(197,211)(198,212)(199,209)(200,210)
(201,215)(202,216)(203,213)(204,214)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,387)(278,388)(279,385)(280,386)(281,391)(282,392)
(283,389)(284,390)(285,395)(286,396)(287,393)(288,394)(289,375)(290,376)
(291,373)(292,374)(293,379)(294,380)(295,377)(296,378)(297,383)(298,384)
(299,381)(300,382)(301,363)(302,364)(303,361)(304,362)(305,367)(306,368)
(307,365)(308,366)(309,371)(310,372)(311,369)(312,370)(313,351)(314,352)
(315,349)(316,350)(317,355)(318,356)(319,353)(320,354)(321,359)(322,360)
(323,357)(324,358)(325,339)(326,340)(327,337)(328,338)(329,343)(330,344)
(331,341)(332,342)(333,347)(334,348)(335,345)(336,346);;
s1 := ( 1, 13)( 2, 14)( 3, 16)( 4, 15)( 5, 21)( 6, 22)( 7, 24)( 8, 23)
( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 25,121)( 26,122)( 27,124)( 28,123)
( 29,129)( 30,130)( 31,132)( 32,131)( 33,125)( 34,126)( 35,128)( 36,127)
( 37,109)( 38,110)( 39,112)( 40,111)( 41,117)( 42,118)( 43,120)( 44,119)
( 45,113)( 46,114)( 47,116)( 48,115)( 49, 97)( 50, 98)( 51,100)( 52, 99)
( 53,105)( 54,106)( 55,108)( 56,107)( 57,101)( 58,102)( 59,104)( 60,103)
( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 65, 93)( 66, 94)( 67, 96)( 68, 95)
( 69, 89)( 70, 90)( 71, 92)( 72, 91)( 75, 76)( 77, 81)( 78, 82)( 79, 84)
( 80, 83)(133,285)(134,286)(135,288)(136,287)(137,281)(138,282)(139,284)
(140,283)(141,277)(142,278)(143,280)(144,279)(145,273)(146,274)(147,276)
(148,275)(149,269)(150,270)(151,272)(152,271)(153,265)(154,266)(155,268)
(156,267)(157,393)(158,394)(159,396)(160,395)(161,389)(162,390)(163,392)
(164,391)(165,385)(166,386)(167,388)(168,387)(169,381)(170,382)(171,384)
(172,383)(173,377)(174,378)(175,380)(176,379)(177,373)(178,374)(179,376)
(180,375)(181,369)(182,370)(183,372)(184,371)(185,365)(186,366)(187,368)
(188,367)(189,361)(190,362)(191,364)(192,363)(193,357)(194,358)(195,360)
(196,359)(197,353)(198,354)(199,356)(200,355)(201,349)(202,350)(203,352)
(204,351)(205,345)(206,346)(207,348)(208,347)(209,341)(210,342)(211,344)
(212,343)(213,337)(214,338)(215,340)(216,339)(217,333)(218,334)(219,336)
(220,335)(221,329)(222,330)(223,332)(224,331)(225,325)(226,326)(227,328)
(228,327)(229,321)(230,322)(231,324)(232,323)(233,317)(234,318)(235,320)
(236,319)(237,313)(238,314)(239,316)(240,315)(241,309)(242,310)(243,312)
(244,311)(245,305)(246,306)(247,308)(248,307)(249,301)(250,302)(251,304)
(252,303)(253,297)(254,298)(255,300)(256,299)(257,293)(258,294)(259,296)
(260,295)(261,289)(262,290)(263,292)(264,291);;
s2 := ( 1,133)( 2,136)( 3,135)( 4,134)( 5,141)( 6,144)( 7,143)( 8,142)
( 9,137)( 10,140)( 11,139)( 12,138)( 13,145)( 14,148)( 15,147)( 16,146)
( 17,153)( 18,156)( 19,155)( 20,154)( 21,149)( 22,152)( 23,151)( 24,150)
( 25,157)( 26,160)( 27,159)( 28,158)( 29,165)( 30,168)( 31,167)( 32,166)
( 33,161)( 34,164)( 35,163)( 36,162)( 37,169)( 38,172)( 39,171)( 40,170)
( 41,177)( 42,180)( 43,179)( 44,178)( 45,173)( 46,176)( 47,175)( 48,174)
( 49,181)( 50,184)( 51,183)( 52,182)( 53,189)( 54,192)( 55,191)( 56,190)
( 57,185)( 58,188)( 59,187)( 60,186)( 61,193)( 62,196)( 63,195)( 64,194)
( 65,201)( 66,204)( 67,203)( 68,202)( 69,197)( 70,200)( 71,199)( 72,198)
( 73,205)( 74,208)( 75,207)( 76,206)( 77,213)( 78,216)( 79,215)( 80,214)
( 81,209)( 82,212)( 83,211)( 84,210)( 85,217)( 86,220)( 87,219)( 88,218)
( 89,225)( 90,228)( 91,227)( 92,226)( 93,221)( 94,224)( 95,223)( 96,222)
( 97,229)( 98,232)( 99,231)(100,230)(101,237)(102,240)(103,239)(104,238)
(105,233)(106,236)(107,235)(108,234)(109,241)(110,244)(111,243)(112,242)
(113,249)(114,252)(115,251)(116,250)(117,245)(118,248)(119,247)(120,246)
(121,253)(122,256)(123,255)(124,254)(125,261)(126,264)(127,263)(128,262)
(129,257)(130,260)(131,259)(132,258)(265,273)(266,276)(267,275)(268,274)
(270,272)(277,285)(278,288)(279,287)(280,286)(282,284)(289,297)(290,300)
(291,299)(292,298)(294,296)(301,309)(302,312)(303,311)(304,310)(306,308)
(313,321)(314,324)(315,323)(316,322)(318,320)(325,333)(326,336)(327,335)
(328,334)(330,332)(337,345)(338,348)(339,347)(340,346)(342,344)(349,357)
(350,360)(351,359)(352,358)(354,356)(361,369)(362,372)(363,371)(364,370)
(366,368)(373,381)(374,384)(375,383)(376,382)(378,380)(385,393)(386,396)
(387,395)(388,394)(390,392);;
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(396)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13,123)
( 14,124)( 15,121)( 16,122)( 17,127)( 18,128)( 19,125)( 20,126)( 21,131)
( 22,132)( 23,129)( 24,130)( 25,111)( 26,112)( 27,109)( 28,110)( 29,115)
( 30,116)( 31,113)( 32,114)( 33,119)( 34,120)( 35,117)( 36,118)( 37, 99)
( 38,100)( 39, 97)( 40, 98)( 41,103)( 42,104)( 43,101)( 44,102)( 45,107)
( 46,108)( 47,105)( 48,106)( 49, 87)( 50, 88)( 51, 85)( 52, 86)( 53, 91)
( 54, 92)( 55, 89)( 56, 90)( 57, 95)( 58, 96)( 59, 93)( 60, 94)( 61, 75)
( 62, 76)( 63, 73)( 64, 74)( 65, 79)( 66, 80)( 67, 77)( 68, 78)( 69, 83)
( 70, 84)( 71, 81)( 72, 82)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,255)(146,256)(147,253)(148,254)(149,259)(150,260)(151,257)
(152,258)(153,263)(154,264)(155,261)(156,262)(157,243)(158,244)(159,241)
(160,242)(161,247)(162,248)(163,245)(164,246)(165,251)(166,252)(167,249)
(168,250)(169,231)(170,232)(171,229)(172,230)(173,235)(174,236)(175,233)
(176,234)(177,239)(178,240)(179,237)(180,238)(181,219)(182,220)(183,217)
(184,218)(185,223)(186,224)(187,221)(188,222)(189,227)(190,228)(191,225)
(192,226)(193,207)(194,208)(195,205)(196,206)(197,211)(198,212)(199,209)
(200,210)(201,215)(202,216)(203,213)(204,214)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,387)(278,388)(279,385)(280,386)(281,391)
(282,392)(283,389)(284,390)(285,395)(286,396)(287,393)(288,394)(289,375)
(290,376)(291,373)(292,374)(293,379)(294,380)(295,377)(296,378)(297,383)
(298,384)(299,381)(300,382)(301,363)(302,364)(303,361)(304,362)(305,367)
(306,368)(307,365)(308,366)(309,371)(310,372)(311,369)(312,370)(313,351)
(314,352)(315,349)(316,350)(317,355)(318,356)(319,353)(320,354)(321,359)
(322,360)(323,357)(324,358)(325,339)(326,340)(327,337)(328,338)(329,343)
(330,344)(331,341)(332,342)(333,347)(334,348)(335,345)(336,346);
s1 := Sym(396)!( 1, 13)( 2, 14)( 3, 16)( 4, 15)( 5, 21)( 6, 22)( 7, 24)
( 8, 23)( 9, 17)( 10, 18)( 11, 20)( 12, 19)( 25,121)( 26,122)( 27,124)
( 28,123)( 29,129)( 30,130)( 31,132)( 32,131)( 33,125)( 34,126)( 35,128)
( 36,127)( 37,109)( 38,110)( 39,112)( 40,111)( 41,117)( 42,118)( 43,120)
( 44,119)( 45,113)( 46,114)( 47,116)( 48,115)( 49, 97)( 50, 98)( 51,100)
( 52, 99)( 53,105)( 54,106)( 55,108)( 56,107)( 57,101)( 58,102)( 59,104)
( 60,103)( 61, 85)( 62, 86)( 63, 88)( 64, 87)( 65, 93)( 66, 94)( 67, 96)
( 68, 95)( 69, 89)( 70, 90)( 71, 92)( 72, 91)( 75, 76)( 77, 81)( 78, 82)
( 79, 84)( 80, 83)(133,285)(134,286)(135,288)(136,287)(137,281)(138,282)
(139,284)(140,283)(141,277)(142,278)(143,280)(144,279)(145,273)(146,274)
(147,276)(148,275)(149,269)(150,270)(151,272)(152,271)(153,265)(154,266)
(155,268)(156,267)(157,393)(158,394)(159,396)(160,395)(161,389)(162,390)
(163,392)(164,391)(165,385)(166,386)(167,388)(168,387)(169,381)(170,382)
(171,384)(172,383)(173,377)(174,378)(175,380)(176,379)(177,373)(178,374)
(179,376)(180,375)(181,369)(182,370)(183,372)(184,371)(185,365)(186,366)
(187,368)(188,367)(189,361)(190,362)(191,364)(192,363)(193,357)(194,358)
(195,360)(196,359)(197,353)(198,354)(199,356)(200,355)(201,349)(202,350)
(203,352)(204,351)(205,345)(206,346)(207,348)(208,347)(209,341)(210,342)
(211,344)(212,343)(213,337)(214,338)(215,340)(216,339)(217,333)(218,334)
(219,336)(220,335)(221,329)(222,330)(223,332)(224,331)(225,325)(226,326)
(227,328)(228,327)(229,321)(230,322)(231,324)(232,323)(233,317)(234,318)
(235,320)(236,319)(237,313)(238,314)(239,316)(240,315)(241,309)(242,310)
(243,312)(244,311)(245,305)(246,306)(247,308)(248,307)(249,301)(250,302)
(251,304)(252,303)(253,297)(254,298)(255,300)(256,299)(257,293)(258,294)
(259,296)(260,295)(261,289)(262,290)(263,292)(264,291);
s2 := Sym(396)!( 1,133)( 2,136)( 3,135)( 4,134)( 5,141)( 6,144)( 7,143)
( 8,142)( 9,137)( 10,140)( 11,139)( 12,138)( 13,145)( 14,148)( 15,147)
( 16,146)( 17,153)( 18,156)( 19,155)( 20,154)( 21,149)( 22,152)( 23,151)
( 24,150)( 25,157)( 26,160)( 27,159)( 28,158)( 29,165)( 30,168)( 31,167)
( 32,166)( 33,161)( 34,164)( 35,163)( 36,162)( 37,169)( 38,172)( 39,171)
( 40,170)( 41,177)( 42,180)( 43,179)( 44,178)( 45,173)( 46,176)( 47,175)
( 48,174)( 49,181)( 50,184)( 51,183)( 52,182)( 53,189)( 54,192)( 55,191)
( 56,190)( 57,185)( 58,188)( 59,187)( 60,186)( 61,193)( 62,196)( 63,195)
( 64,194)( 65,201)( 66,204)( 67,203)( 68,202)( 69,197)( 70,200)( 71,199)
( 72,198)( 73,205)( 74,208)( 75,207)( 76,206)( 77,213)( 78,216)( 79,215)
( 80,214)( 81,209)( 82,212)( 83,211)( 84,210)( 85,217)( 86,220)( 87,219)
( 88,218)( 89,225)( 90,228)( 91,227)( 92,226)( 93,221)( 94,224)( 95,223)
( 96,222)( 97,229)( 98,232)( 99,231)(100,230)(101,237)(102,240)(103,239)
(104,238)(105,233)(106,236)(107,235)(108,234)(109,241)(110,244)(111,243)
(112,242)(113,249)(114,252)(115,251)(116,250)(117,245)(118,248)(119,247)
(120,246)(121,253)(122,256)(123,255)(124,254)(125,261)(126,264)(127,263)
(128,262)(129,257)(130,260)(131,259)(132,258)(265,273)(266,276)(267,275)
(268,274)(270,272)(277,285)(278,288)(279,287)(280,286)(282,284)(289,297)
(290,300)(291,299)(292,298)(294,296)(301,309)(302,312)(303,311)(304,310)
(306,308)(313,321)(314,324)(315,323)(316,322)(318,320)(325,333)(326,336)
(327,335)(328,334)(330,332)(337,345)(338,348)(339,347)(340,346)(342,344)
(349,357)(350,360)(351,359)(352,358)(354,356)(361,369)(362,372)(363,371)
(364,370)(366,368)(373,381)(374,384)(375,383)(376,382)(378,380)(385,393)
(386,396)(387,395)(388,394)(390,392);
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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2 >;
References : None.
to this polytope