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