Polytope of Type {18,44}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,44}*1584a
Also Known As : {18,44|2}. if this polytope has another name.
Group : SmallGroup(1584,114)
Rank : 3
Schlafli Type : {18,44}
Number of vertices, edges, etc : 18, 396, 44
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 : {18,22}*792
3-fold quotients : {6,44}*528a
6-fold quotients : {6,22}*264
9-fold quotients : {2,44}*176
11-fold quotients : {18,4}*144a
18-fold quotients : {2,22}*88
22-fold quotients : {18,2}*72
33-fold quotients : {6,4}*48a
36-fold quotients : {2,11}*44
44-fold quotients : {9,2}*36
66-fold quotients : {6,2}*24
99-fold quotients : {2,4}*16
132-fold quotients : {3,2}*12
198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)( 23, 24)
( 26, 27)( 29, 30)( 32, 33)( 34, 69)( 35, 68)( 36, 67)( 37, 72)( 38, 71)
( 39, 70)( 40, 75)( 41, 74)( 42, 73)( 43, 78)( 44, 77)( 45, 76)( 46, 81)
( 47, 80)( 48, 79)( 49, 84)( 50, 83)( 51, 82)( 52, 87)( 53, 86)( 54, 85)
( 55, 90)( 56, 89)( 57, 88)( 58, 93)( 59, 92)( 60, 91)( 61, 96)( 62, 95)
( 63, 94)( 64, 99)( 65, 98)( 66, 97)(101,102)(104,105)(107,108)(110,111)
(113,114)(116,117)(119,120)(122,123)(125,126)(128,129)(131,132)(133,168)
(134,167)(135,166)(136,171)(137,170)(138,169)(139,174)(140,173)(141,172)
(142,177)(143,176)(144,175)(145,180)(146,179)(147,178)(148,183)(149,182)
(150,181)(151,186)(152,185)(153,184)(154,189)(155,188)(156,187)(157,192)
(158,191)(159,190)(160,195)(161,194)(162,193)(163,198)(164,197)(165,196)
(200,201)(203,204)(206,207)(209,210)(212,213)(215,216)(218,219)(221,222)
(224,225)(227,228)(230,231)(232,267)(233,266)(234,265)(235,270)(236,269)
(237,268)(238,273)(239,272)(240,271)(241,276)(242,275)(243,274)(244,279)
(245,278)(246,277)(247,282)(248,281)(249,280)(250,285)(251,284)(252,283)
(253,288)(254,287)(255,286)(256,291)(257,290)(258,289)(259,294)(260,293)
(261,292)(262,297)(263,296)(264,295)(299,300)(302,303)(305,306)(308,309)
(311,312)(314,315)(317,318)(320,321)(323,324)(326,327)(329,330)(331,366)
(332,365)(333,364)(334,369)(335,368)(336,367)(337,372)(338,371)(339,370)
(340,375)(341,374)(342,373)(343,378)(344,377)(345,376)(346,381)(347,380)
(348,379)(349,384)(350,383)(351,382)(352,387)(353,386)(354,385)(355,390)
(356,389)(357,388)(358,393)(359,392)(360,391)(361,396)(362,395)(363,394);;
s1 := ( 1, 34)( 2, 36)( 3, 35)( 4, 64)( 5, 66)( 6, 65)( 7, 61)( 8, 63)
( 9, 62)( 10, 58)( 11, 60)( 12, 59)( 13, 55)( 14, 57)( 15, 56)( 16, 52)
( 17, 54)( 18, 53)( 19, 49)( 20, 51)( 21, 50)( 22, 46)( 23, 48)( 24, 47)
( 25, 43)( 26, 45)( 27, 44)( 28, 40)( 29, 42)( 30, 41)( 31, 37)( 32, 39)
( 33, 38)( 67, 69)( 70, 99)( 71, 98)( 72, 97)( 73, 96)( 74, 95)( 75, 94)
( 76, 93)( 77, 92)( 78, 91)( 79, 90)( 80, 89)( 81, 88)( 82, 87)( 83, 86)
( 84, 85)(100,133)(101,135)(102,134)(103,163)(104,165)(105,164)(106,160)
(107,162)(108,161)(109,157)(110,159)(111,158)(112,154)(113,156)(114,155)
(115,151)(116,153)(117,152)(118,148)(119,150)(120,149)(121,145)(122,147)
(123,146)(124,142)(125,144)(126,143)(127,139)(128,141)(129,140)(130,136)
(131,138)(132,137)(166,168)(169,198)(170,197)(171,196)(172,195)(173,194)
(174,193)(175,192)(176,191)(177,190)(178,189)(179,188)(180,187)(181,186)
(182,185)(183,184)(199,331)(200,333)(201,332)(202,361)(203,363)(204,362)
(205,358)(206,360)(207,359)(208,355)(209,357)(210,356)(211,352)(212,354)
(213,353)(214,349)(215,351)(216,350)(217,346)(218,348)(219,347)(220,343)
(221,345)(222,344)(223,340)(224,342)(225,341)(226,337)(227,339)(228,338)
(229,334)(230,336)(231,335)(232,298)(233,300)(234,299)(235,328)(236,330)
(237,329)(238,325)(239,327)(240,326)(241,322)(242,324)(243,323)(244,319)
(245,321)(246,320)(247,316)(248,318)(249,317)(250,313)(251,315)(252,314)
(253,310)(254,312)(255,311)(256,307)(257,309)(258,308)(259,304)(260,306)
(261,305)(262,301)(263,303)(264,302)(265,366)(266,365)(267,364)(268,396)
(269,395)(270,394)(271,393)(272,392)(273,391)(274,390)(275,389)(276,388)
(277,387)(278,386)(279,385)(280,384)(281,383)(282,382)(283,381)(284,380)
(285,379)(286,378)(287,377)(288,376)(289,375)(290,374)(291,373)(292,372)
(293,371)(294,370)(295,369)(296,368)(297,367);;
s2 := ( 1,202)( 2,203)( 3,204)( 4,199)( 5,200)( 6,201)( 7,229)( 8,230)
( 9,231)( 10,226)( 11,227)( 12,228)( 13,223)( 14,224)( 15,225)( 16,220)
( 17,221)( 18,222)( 19,217)( 20,218)( 21,219)( 22,214)( 23,215)( 24,216)
( 25,211)( 26,212)( 27,213)( 28,208)( 29,209)( 30,210)( 31,205)( 32,206)
( 33,207)( 34,235)( 35,236)( 36,237)( 37,232)( 38,233)( 39,234)( 40,262)
( 41,263)( 42,264)( 43,259)( 44,260)( 45,261)( 46,256)( 47,257)( 48,258)
( 49,253)( 50,254)( 51,255)( 52,250)( 53,251)( 54,252)( 55,247)( 56,248)
( 57,249)( 58,244)( 59,245)( 60,246)( 61,241)( 62,242)( 63,243)( 64,238)
( 65,239)( 66,240)( 67,268)( 68,269)( 69,270)( 70,265)( 71,266)( 72,267)
( 73,295)( 74,296)( 75,297)( 76,292)( 77,293)( 78,294)( 79,289)( 80,290)
( 81,291)( 82,286)( 83,287)( 84,288)( 85,283)( 86,284)( 87,285)( 88,280)
( 89,281)( 90,282)( 91,277)( 92,278)( 93,279)( 94,274)( 95,275)( 96,276)
( 97,271)( 98,272)( 99,273)(100,301)(101,302)(102,303)(103,298)(104,299)
(105,300)(106,328)(107,329)(108,330)(109,325)(110,326)(111,327)(112,322)
(113,323)(114,324)(115,319)(116,320)(117,321)(118,316)(119,317)(120,318)
(121,313)(122,314)(123,315)(124,310)(125,311)(126,312)(127,307)(128,308)
(129,309)(130,304)(131,305)(132,306)(133,334)(134,335)(135,336)(136,331)
(137,332)(138,333)(139,361)(140,362)(141,363)(142,358)(143,359)(144,360)
(145,355)(146,356)(147,357)(148,352)(149,353)(150,354)(151,349)(152,350)
(153,351)(154,346)(155,347)(156,348)(157,343)(158,344)(159,345)(160,340)
(161,341)(162,342)(163,337)(164,338)(165,339)(166,367)(167,368)(168,369)
(169,364)(170,365)(171,366)(172,394)(173,395)(174,396)(175,391)(176,392)
(177,393)(178,388)(179,389)(180,390)(181,385)(182,386)(183,387)(184,382)
(185,383)(186,384)(187,379)(188,380)(189,381)(190,376)(191,377)(192,378)
(193,373)(194,374)(195,375)(196,370)(197,371)(198,372);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(396)!( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 20, 21)
( 23, 24)( 26, 27)( 29, 30)( 32, 33)( 34, 69)( 35, 68)( 36, 67)( 37, 72)
( 38, 71)( 39, 70)( 40, 75)( 41, 74)( 42, 73)( 43, 78)( 44, 77)( 45, 76)
( 46, 81)( 47, 80)( 48, 79)( 49, 84)( 50, 83)( 51, 82)( 52, 87)( 53, 86)
( 54, 85)( 55, 90)( 56, 89)( 57, 88)( 58, 93)( 59, 92)( 60, 91)( 61, 96)
( 62, 95)( 63, 94)( 64, 99)( 65, 98)( 66, 97)(101,102)(104,105)(107,108)
(110,111)(113,114)(116,117)(119,120)(122,123)(125,126)(128,129)(131,132)
(133,168)(134,167)(135,166)(136,171)(137,170)(138,169)(139,174)(140,173)
(141,172)(142,177)(143,176)(144,175)(145,180)(146,179)(147,178)(148,183)
(149,182)(150,181)(151,186)(152,185)(153,184)(154,189)(155,188)(156,187)
(157,192)(158,191)(159,190)(160,195)(161,194)(162,193)(163,198)(164,197)
(165,196)(200,201)(203,204)(206,207)(209,210)(212,213)(215,216)(218,219)
(221,222)(224,225)(227,228)(230,231)(232,267)(233,266)(234,265)(235,270)
(236,269)(237,268)(238,273)(239,272)(240,271)(241,276)(242,275)(243,274)
(244,279)(245,278)(246,277)(247,282)(248,281)(249,280)(250,285)(251,284)
(252,283)(253,288)(254,287)(255,286)(256,291)(257,290)(258,289)(259,294)
(260,293)(261,292)(262,297)(263,296)(264,295)(299,300)(302,303)(305,306)
(308,309)(311,312)(314,315)(317,318)(320,321)(323,324)(326,327)(329,330)
(331,366)(332,365)(333,364)(334,369)(335,368)(336,367)(337,372)(338,371)
(339,370)(340,375)(341,374)(342,373)(343,378)(344,377)(345,376)(346,381)
(347,380)(348,379)(349,384)(350,383)(351,382)(352,387)(353,386)(354,385)
(355,390)(356,389)(357,388)(358,393)(359,392)(360,391)(361,396)(362,395)
(363,394);
s1 := Sym(396)!( 1, 34)( 2, 36)( 3, 35)( 4, 64)( 5, 66)( 6, 65)( 7, 61)
( 8, 63)( 9, 62)( 10, 58)( 11, 60)( 12, 59)( 13, 55)( 14, 57)( 15, 56)
( 16, 52)( 17, 54)( 18, 53)( 19, 49)( 20, 51)( 21, 50)( 22, 46)( 23, 48)
( 24, 47)( 25, 43)( 26, 45)( 27, 44)( 28, 40)( 29, 42)( 30, 41)( 31, 37)
( 32, 39)( 33, 38)( 67, 69)( 70, 99)( 71, 98)( 72, 97)( 73, 96)( 74, 95)
( 75, 94)( 76, 93)( 77, 92)( 78, 91)( 79, 90)( 80, 89)( 81, 88)( 82, 87)
( 83, 86)( 84, 85)(100,133)(101,135)(102,134)(103,163)(104,165)(105,164)
(106,160)(107,162)(108,161)(109,157)(110,159)(111,158)(112,154)(113,156)
(114,155)(115,151)(116,153)(117,152)(118,148)(119,150)(120,149)(121,145)
(122,147)(123,146)(124,142)(125,144)(126,143)(127,139)(128,141)(129,140)
(130,136)(131,138)(132,137)(166,168)(169,198)(170,197)(171,196)(172,195)
(173,194)(174,193)(175,192)(176,191)(177,190)(178,189)(179,188)(180,187)
(181,186)(182,185)(183,184)(199,331)(200,333)(201,332)(202,361)(203,363)
(204,362)(205,358)(206,360)(207,359)(208,355)(209,357)(210,356)(211,352)
(212,354)(213,353)(214,349)(215,351)(216,350)(217,346)(218,348)(219,347)
(220,343)(221,345)(222,344)(223,340)(224,342)(225,341)(226,337)(227,339)
(228,338)(229,334)(230,336)(231,335)(232,298)(233,300)(234,299)(235,328)
(236,330)(237,329)(238,325)(239,327)(240,326)(241,322)(242,324)(243,323)
(244,319)(245,321)(246,320)(247,316)(248,318)(249,317)(250,313)(251,315)
(252,314)(253,310)(254,312)(255,311)(256,307)(257,309)(258,308)(259,304)
(260,306)(261,305)(262,301)(263,303)(264,302)(265,366)(266,365)(267,364)
(268,396)(269,395)(270,394)(271,393)(272,392)(273,391)(274,390)(275,389)
(276,388)(277,387)(278,386)(279,385)(280,384)(281,383)(282,382)(283,381)
(284,380)(285,379)(286,378)(287,377)(288,376)(289,375)(290,374)(291,373)
(292,372)(293,371)(294,370)(295,369)(296,368)(297,367);
s2 := Sym(396)!( 1,202)( 2,203)( 3,204)( 4,199)( 5,200)( 6,201)( 7,229)
( 8,230)( 9,231)( 10,226)( 11,227)( 12,228)( 13,223)( 14,224)( 15,225)
( 16,220)( 17,221)( 18,222)( 19,217)( 20,218)( 21,219)( 22,214)( 23,215)
( 24,216)( 25,211)( 26,212)( 27,213)( 28,208)( 29,209)( 30,210)( 31,205)
( 32,206)( 33,207)( 34,235)( 35,236)( 36,237)( 37,232)( 38,233)( 39,234)
( 40,262)( 41,263)( 42,264)( 43,259)( 44,260)( 45,261)( 46,256)( 47,257)
( 48,258)( 49,253)( 50,254)( 51,255)( 52,250)( 53,251)( 54,252)( 55,247)
( 56,248)( 57,249)( 58,244)( 59,245)( 60,246)( 61,241)( 62,242)( 63,243)
( 64,238)( 65,239)( 66,240)( 67,268)( 68,269)( 69,270)( 70,265)( 71,266)
( 72,267)( 73,295)( 74,296)( 75,297)( 76,292)( 77,293)( 78,294)( 79,289)
( 80,290)( 81,291)( 82,286)( 83,287)( 84,288)( 85,283)( 86,284)( 87,285)
( 88,280)( 89,281)( 90,282)( 91,277)( 92,278)( 93,279)( 94,274)( 95,275)
( 96,276)( 97,271)( 98,272)( 99,273)(100,301)(101,302)(102,303)(103,298)
(104,299)(105,300)(106,328)(107,329)(108,330)(109,325)(110,326)(111,327)
(112,322)(113,323)(114,324)(115,319)(116,320)(117,321)(118,316)(119,317)
(120,318)(121,313)(122,314)(123,315)(124,310)(125,311)(126,312)(127,307)
(128,308)(129,309)(130,304)(131,305)(132,306)(133,334)(134,335)(135,336)
(136,331)(137,332)(138,333)(139,361)(140,362)(141,363)(142,358)(143,359)
(144,360)(145,355)(146,356)(147,357)(148,352)(149,353)(150,354)(151,349)
(152,350)(153,351)(154,346)(155,347)(156,348)(157,343)(158,344)(159,345)
(160,340)(161,341)(162,342)(163,337)(164,338)(165,339)(166,367)(167,368)
(168,369)(169,364)(170,365)(171,366)(172,394)(173,395)(174,396)(175,391)
(176,392)(177,393)(178,388)(179,389)(180,390)(181,385)(182,386)(183,387)
(184,382)(185,383)(186,384)(187,379)(188,380)(189,381)(190,376)(191,377)
(192,378)(193,373)(194,374)(195,375)(196,370)(197,371)(198,372);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope