Polytope of Type {36,22}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,22}*1584
Also Known As : {36,22|2}. if this polytope has another name.
Group : SmallGroup(1584,113)
Rank : 3
Schlafli Type : {36,22}
Number of vertices, edges, etc : 36, 396, 22
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 : {12,22}*528
   6-fold quotients : {6,22}*264
   9-fold quotients : {4,22}*176
   11-fold quotients : {36,2}*144
   18-fold quotients : {2,22}*88
   22-fold quotients : {18,2}*72
   33-fold quotients : {12,2}*48
   36-fold quotients : {2,11}*44
   44-fold quotients : {9,2}*36
   66-fold quotients : {6,2}*24
   99-fold quotients : {4,2}*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)
(199,298)(200,300)(201,299)(202,301)(203,303)(204,302)(205,304)(206,306)
(207,305)(208,307)(209,309)(210,308)(211,310)(212,312)(213,311)(214,313)
(215,315)(216,314)(217,316)(218,318)(219,317)(220,319)(221,321)(222,320)
(223,322)(224,324)(225,323)(226,325)(227,327)(228,326)(229,328)(230,330)
(231,329)(232,366)(233,365)(234,364)(235,369)(236,368)(237,367)(238,372)
(239,371)(240,370)(241,375)(242,374)(243,373)(244,378)(245,377)(246,376)
(247,381)(248,380)(249,379)(250,384)(251,383)(252,382)(253,387)(254,386)
(255,385)(256,390)(257,389)(258,388)(259,393)(260,392)(261,391)(262,396)
(263,395)(264,394)(265,333)(266,332)(267,331)(268,336)(269,335)(270,334)
(271,339)(272,338)(273,337)(274,342)(275,341)(276,340)(277,345)(278,344)
(279,343)(280,348)(281,347)(282,346)(283,351)(284,350)(285,349)(286,354)
(287,353)(288,352)(289,357)(290,356)(291,355)(292,360)(293,359)(294,358)
(295,363)(296,362)(297,361);;
s1 := (  1,232)(  2,234)(  3,233)(  4,262)(  5,264)(  6,263)(  7,259)(  8,261)
(  9,260)( 10,256)( 11,258)( 12,257)( 13,253)( 14,255)( 15,254)( 16,250)
( 17,252)( 18,251)( 19,247)( 20,249)( 21,248)( 22,244)( 23,246)( 24,245)
( 25,241)( 26,243)( 27,242)( 28,238)( 29,240)( 30,239)( 31,235)( 32,237)
( 33,236)( 34,199)( 35,201)( 36,200)( 37,229)( 38,231)( 39,230)( 40,226)
( 41,228)( 42,227)( 43,223)( 44,225)( 45,224)( 46,220)( 47,222)( 48,221)
( 49,217)( 50,219)( 51,218)( 52,214)( 53,216)( 54,215)( 55,211)( 56,213)
( 57,212)( 58,208)( 59,210)( 60,209)( 61,205)( 62,207)( 63,206)( 64,202)
( 65,204)( 66,203)( 67,267)( 68,266)( 69,265)( 70,297)( 71,296)( 72,295)
( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,289)( 79,288)( 80,287)
( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)( 88,279)
( 89,278)( 90,277)( 91,276)( 92,275)( 93,274)( 94,273)( 95,272)( 96,271)
( 97,270)( 98,269)( 99,268)(100,331)(101,333)(102,332)(103,361)(104,363)
(105,362)(106,358)(107,360)(108,359)(109,355)(110,357)(111,356)(112,352)
(113,354)(114,353)(115,349)(116,351)(117,350)(118,346)(119,348)(120,347)
(121,343)(122,345)(123,344)(124,340)(125,342)(126,341)(127,337)(128,339)
(129,338)(130,334)(131,336)(132,335)(133,298)(134,300)(135,299)(136,328)
(137,330)(138,329)(139,325)(140,327)(141,326)(142,322)(143,324)(144,323)
(145,319)(146,321)(147,320)(148,316)(149,318)(150,317)(151,313)(152,315)
(153,314)(154,310)(155,312)(156,311)(157,307)(158,309)(159,308)(160,304)
(161,306)(162,305)(163,301)(164,303)(165,302)(166,366)(167,365)(168,364)
(169,396)(170,395)(171,394)(172,393)(173,392)(174,391)(175,390)(176,389)
(177,388)(178,387)(179,386)(180,385)(181,384)(182,383)(183,382)(184,381)
(185,380)(186,379)(187,378)(188,377)(189,376)(190,375)(191,374)(192,373)
(193,372)(194,371)(195,370)(196,369)(197,368)(198,367);;
s2 := (  1,  4)(  2,  5)(  3,  6)(  7, 31)(  8, 32)(  9, 33)( 10, 28)( 11, 29)
( 12, 30)( 13, 25)( 14, 26)( 15, 27)( 16, 22)( 17, 23)( 18, 24)( 34, 37)
( 35, 38)( 36, 39)( 40, 64)( 41, 65)( 42, 66)( 43, 61)( 44, 62)( 45, 63)
( 46, 58)( 47, 59)( 48, 60)( 49, 55)( 50, 56)( 51, 57)( 67, 70)( 68, 71)
( 69, 72)( 73, 97)( 74, 98)( 75, 99)( 76, 94)( 77, 95)( 78, 96)( 79, 91)
( 80, 92)( 81, 93)( 82, 88)( 83, 89)( 84, 90)(100,103)(101,104)(102,105)
(106,130)(107,131)(108,132)(109,127)(110,128)(111,129)(112,124)(113,125)
(114,126)(115,121)(116,122)(117,123)(133,136)(134,137)(135,138)(139,163)
(140,164)(141,165)(142,160)(143,161)(144,162)(145,157)(146,158)(147,159)
(148,154)(149,155)(150,156)(166,169)(167,170)(168,171)(172,196)(173,197)
(174,198)(175,193)(176,194)(177,195)(178,190)(179,191)(180,192)(181,187)
(182,188)(183,189)(199,202)(200,203)(201,204)(205,229)(206,230)(207,231)
(208,226)(209,227)(210,228)(211,223)(212,224)(213,225)(214,220)(215,221)
(216,222)(232,235)(233,236)(234,237)(238,262)(239,263)(240,264)(241,259)
(242,260)(243,261)(244,256)(245,257)(246,258)(247,253)(248,254)(249,255)
(265,268)(266,269)(267,270)(271,295)(272,296)(273,297)(274,292)(275,293)
(276,294)(277,289)(278,290)(279,291)(280,286)(281,287)(282,288)(298,301)
(299,302)(300,303)(304,328)(305,329)(306,330)(307,325)(308,326)(309,327)
(310,322)(311,323)(312,324)(313,319)(314,320)(315,321)(331,334)(332,335)
(333,336)(337,361)(338,362)(339,363)(340,358)(341,359)(342,360)(343,355)
(344,356)(345,357)(346,352)(347,353)(348,354)(364,367)(365,368)(366,369)
(370,394)(371,395)(372,396)(373,391)(374,392)(375,393)(376,388)(377,389)
(378,390)(379,385)(380,386)(381,387);;
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*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 ];;
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)(199,298)(200,300)(201,299)(202,301)(203,303)(204,302)(205,304)
(206,306)(207,305)(208,307)(209,309)(210,308)(211,310)(212,312)(213,311)
(214,313)(215,315)(216,314)(217,316)(218,318)(219,317)(220,319)(221,321)
(222,320)(223,322)(224,324)(225,323)(226,325)(227,327)(228,326)(229,328)
(230,330)(231,329)(232,366)(233,365)(234,364)(235,369)(236,368)(237,367)
(238,372)(239,371)(240,370)(241,375)(242,374)(243,373)(244,378)(245,377)
(246,376)(247,381)(248,380)(249,379)(250,384)(251,383)(252,382)(253,387)
(254,386)(255,385)(256,390)(257,389)(258,388)(259,393)(260,392)(261,391)
(262,396)(263,395)(264,394)(265,333)(266,332)(267,331)(268,336)(269,335)
(270,334)(271,339)(272,338)(273,337)(274,342)(275,341)(276,340)(277,345)
(278,344)(279,343)(280,348)(281,347)(282,346)(283,351)(284,350)(285,349)
(286,354)(287,353)(288,352)(289,357)(290,356)(291,355)(292,360)(293,359)
(294,358)(295,363)(296,362)(297,361);
s1 := Sym(396)!(  1,232)(  2,234)(  3,233)(  4,262)(  5,264)(  6,263)(  7,259)
(  8,261)(  9,260)( 10,256)( 11,258)( 12,257)( 13,253)( 14,255)( 15,254)
( 16,250)( 17,252)( 18,251)( 19,247)( 20,249)( 21,248)( 22,244)( 23,246)
( 24,245)( 25,241)( 26,243)( 27,242)( 28,238)( 29,240)( 30,239)( 31,235)
( 32,237)( 33,236)( 34,199)( 35,201)( 36,200)( 37,229)( 38,231)( 39,230)
( 40,226)( 41,228)( 42,227)( 43,223)( 44,225)( 45,224)( 46,220)( 47,222)
( 48,221)( 49,217)( 50,219)( 51,218)( 52,214)( 53,216)( 54,215)( 55,211)
( 56,213)( 57,212)( 58,208)( 59,210)( 60,209)( 61,205)( 62,207)( 63,206)
( 64,202)( 65,204)( 66,203)( 67,267)( 68,266)( 69,265)( 70,297)( 71,296)
( 72,295)( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,289)( 79,288)
( 80,287)( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)
( 88,279)( 89,278)( 90,277)( 91,276)( 92,275)( 93,274)( 94,273)( 95,272)
( 96,271)( 97,270)( 98,269)( 99,268)(100,331)(101,333)(102,332)(103,361)
(104,363)(105,362)(106,358)(107,360)(108,359)(109,355)(110,357)(111,356)
(112,352)(113,354)(114,353)(115,349)(116,351)(117,350)(118,346)(119,348)
(120,347)(121,343)(122,345)(123,344)(124,340)(125,342)(126,341)(127,337)
(128,339)(129,338)(130,334)(131,336)(132,335)(133,298)(134,300)(135,299)
(136,328)(137,330)(138,329)(139,325)(140,327)(141,326)(142,322)(143,324)
(144,323)(145,319)(146,321)(147,320)(148,316)(149,318)(150,317)(151,313)
(152,315)(153,314)(154,310)(155,312)(156,311)(157,307)(158,309)(159,308)
(160,304)(161,306)(162,305)(163,301)(164,303)(165,302)(166,366)(167,365)
(168,364)(169,396)(170,395)(171,394)(172,393)(173,392)(174,391)(175,390)
(176,389)(177,388)(178,387)(179,386)(180,385)(181,384)(182,383)(183,382)
(184,381)(185,380)(186,379)(187,378)(188,377)(189,376)(190,375)(191,374)
(192,373)(193,372)(194,371)(195,370)(196,369)(197,368)(198,367);
s2 := Sym(396)!(  1,  4)(  2,  5)(  3,  6)(  7, 31)(  8, 32)(  9, 33)( 10, 28)
( 11, 29)( 12, 30)( 13, 25)( 14, 26)( 15, 27)( 16, 22)( 17, 23)( 18, 24)
( 34, 37)( 35, 38)( 36, 39)( 40, 64)( 41, 65)( 42, 66)( 43, 61)( 44, 62)
( 45, 63)( 46, 58)( 47, 59)( 48, 60)( 49, 55)( 50, 56)( 51, 57)( 67, 70)
( 68, 71)( 69, 72)( 73, 97)( 74, 98)( 75, 99)( 76, 94)( 77, 95)( 78, 96)
( 79, 91)( 80, 92)( 81, 93)( 82, 88)( 83, 89)( 84, 90)(100,103)(101,104)
(102,105)(106,130)(107,131)(108,132)(109,127)(110,128)(111,129)(112,124)
(113,125)(114,126)(115,121)(116,122)(117,123)(133,136)(134,137)(135,138)
(139,163)(140,164)(141,165)(142,160)(143,161)(144,162)(145,157)(146,158)
(147,159)(148,154)(149,155)(150,156)(166,169)(167,170)(168,171)(172,196)
(173,197)(174,198)(175,193)(176,194)(177,195)(178,190)(179,191)(180,192)
(181,187)(182,188)(183,189)(199,202)(200,203)(201,204)(205,229)(206,230)
(207,231)(208,226)(209,227)(210,228)(211,223)(212,224)(213,225)(214,220)
(215,221)(216,222)(232,235)(233,236)(234,237)(238,262)(239,263)(240,264)
(241,259)(242,260)(243,261)(244,256)(245,257)(246,258)(247,253)(248,254)
(249,255)(265,268)(266,269)(267,270)(271,295)(272,296)(273,297)(274,292)
(275,293)(276,294)(277,289)(278,290)(279,291)(280,286)(281,287)(282,288)
(298,301)(299,302)(300,303)(304,328)(305,329)(306,330)(307,325)(308,326)
(309,327)(310,322)(311,323)(312,324)(313,319)(314,320)(315,321)(331,334)
(332,335)(333,336)(337,361)(338,362)(339,363)(340,358)(341,359)(342,360)
(343,355)(344,356)(345,357)(346,352)(347,353)(348,354)(364,367)(365,368)
(366,369)(370,394)(371,395)(372,396)(373,391)(374,392)(375,393)(376,388)
(377,389)(378,390)(379,385)(380,386)(381,387);
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*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 >;

References : None.
to this polytope