Polytope of Type {66,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {66,12}*1584b
Also Known As : {66,12|2}. if this polytope has another name.
Group : SmallGroup(1584,561)
Rank : 3
Schlafli Type : {66,12}
Number of vertices, edges, etc : 66, 396, 12
Order of s0s1s2 : 132
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 : {66,6}*792b
3-fold quotients : {22,12}*528, {66,4}*528a
6-fold quotients : {22,6}*264, {66,2}*264
9-fold quotients : {22,4}*176
11-fold quotients : {6,12}*144a
12-fold quotients : {33,2}*132
18-fold quotients : {22,2}*88
22-fold quotients : {6,6}*72a
33-fold quotients : {2,12}*48, {6,4}*48a
36-fold quotients : {11,2}*44
66-fold quotients : {2,6}*24, {6,2}*24
99-fold quotients : {2,4}*16
132-fold quotients : {2,3}*12, {3,2}*12
198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 12, 23)( 13, 33)( 14, 32)
( 15, 31)( 16, 30)( 17, 29)( 18, 28)( 19, 27)( 20, 26)( 21, 25)( 22, 24)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)( 47, 65)
( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)( 55, 57)
( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 78, 89)( 79, 99)( 80, 98)
( 81, 97)( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)( 88, 90)
(101,110)(102,109)(103,108)(104,107)(105,106)(111,122)(112,132)(113,131)
(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)(121,123)
(134,143)(135,142)(136,141)(137,140)(138,139)(144,155)(145,165)(146,164)
(147,163)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)
(167,176)(168,175)(169,174)(170,173)(171,172)(177,188)(178,198)(179,197)
(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)(187,189)
(200,209)(201,208)(202,207)(203,206)(204,205)(210,221)(211,231)(212,230)
(213,229)(214,228)(215,227)(216,226)(217,225)(218,224)(219,223)(220,222)
(233,242)(234,241)(235,240)(236,239)(237,238)(243,254)(244,264)(245,263)
(246,262)(247,261)(248,260)(249,259)(250,258)(251,257)(252,256)(253,255)
(266,275)(267,274)(268,273)(269,272)(270,271)(276,287)(277,297)(278,296)
(279,295)(280,294)(281,293)(282,292)(283,291)(284,290)(285,289)(286,288)
(299,308)(300,307)(301,306)(302,305)(303,304)(309,320)(310,330)(311,329)
(312,328)(313,327)(314,326)(315,325)(316,324)(317,323)(318,322)(319,321)
(332,341)(333,340)(334,339)(335,338)(336,337)(342,353)(343,363)(344,362)
(345,361)(346,360)(347,359)(348,358)(349,357)(350,356)(351,355)(352,354)
(365,374)(366,373)(367,372)(368,371)(369,370)(375,386)(376,396)(377,395)
(378,394)(379,393)(380,392)(381,391)(382,390)(383,389)(384,388)(385,387);;
s1 := ( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)
( 9, 16)( 10, 15)( 11, 14)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 34, 79)( 35, 78)( 36, 88)( 37, 87)( 38, 86)( 39, 85)( 40, 84)( 41, 83)
( 42, 82)( 43, 81)( 44, 80)( 45, 68)( 46, 67)( 47, 77)( 48, 76)( 49, 75)
( 50, 74)( 51, 73)( 52, 72)( 53, 71)( 54, 70)( 55, 69)( 56, 90)( 57, 89)
( 58, 99)( 59, 98)( 60, 97)( 61, 96)( 62, 95)( 63, 94)( 64, 93)( 65, 92)
( 66, 91)(100,112)(101,111)(102,121)(103,120)(104,119)(105,118)(106,117)
(107,116)(108,115)(109,114)(110,113)(122,123)(124,132)(125,131)(126,130)
(127,129)(133,178)(134,177)(135,187)(136,186)(137,185)(138,184)(139,183)
(140,182)(141,181)(142,180)(143,179)(144,167)(145,166)(146,176)(147,175)
(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,189)
(156,188)(157,198)(158,197)(159,196)(160,195)(161,194)(162,193)(163,192)
(164,191)(165,190)(199,310)(200,309)(201,319)(202,318)(203,317)(204,316)
(205,315)(206,314)(207,313)(208,312)(209,311)(210,299)(211,298)(212,308)
(213,307)(214,306)(215,305)(216,304)(217,303)(218,302)(219,301)(220,300)
(221,321)(222,320)(223,330)(224,329)(225,328)(226,327)(227,326)(228,325)
(229,324)(230,323)(231,322)(232,376)(233,375)(234,385)(235,384)(236,383)
(237,382)(238,381)(239,380)(240,379)(241,378)(242,377)(243,365)(244,364)
(245,374)(246,373)(247,372)(248,371)(249,370)(250,369)(251,368)(252,367)
(253,366)(254,387)(255,386)(256,396)(257,395)(258,394)(259,393)(260,392)
(261,391)(262,390)(263,389)(264,388)(265,343)(266,342)(267,352)(268,351)
(269,350)(270,349)(271,348)(272,347)(273,346)(274,345)(275,344)(276,332)
(277,331)(278,341)(279,340)(280,339)(281,338)(282,337)(283,336)(284,335)
(285,334)(286,333)(287,354)(288,353)(289,363)(290,362)(291,361)(292,360)
(293,359)(294,358)(295,357)(296,356)(297,355);;
s2 := ( 1,232)( 2,233)( 3,234)( 4,235)( 5,236)( 6,237)( 7,238)( 8,239)
( 9,240)( 10,241)( 11,242)( 12,243)( 13,244)( 14,245)( 15,246)( 16,247)
( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,253)( 23,254)( 24,255)
( 25,256)( 26,257)( 27,258)( 28,259)( 29,260)( 30,261)( 31,262)( 32,263)
( 33,264)( 34,199)( 35,200)( 36,201)( 37,202)( 38,203)( 39,204)( 40,205)
( 41,206)( 42,207)( 43,208)( 44,209)( 45,210)( 46,211)( 47,212)( 48,213)
( 49,214)( 50,215)( 51,216)( 52,217)( 53,218)( 54,219)( 55,220)( 56,221)
( 57,222)( 58,223)( 59,224)( 60,225)( 61,226)( 62,227)( 63,228)( 64,229)
( 65,230)( 66,231)( 67,265)( 68,266)( 69,267)( 70,268)( 71,269)( 72,270)
( 73,271)( 74,272)( 75,273)( 76,274)( 77,275)( 78,276)( 79,277)( 80,278)
( 81,279)( 82,280)( 83,281)( 84,282)( 85,283)( 86,284)( 87,285)( 88,286)
( 89,287)( 90,288)( 91,289)( 92,290)( 93,291)( 94,292)( 95,293)( 96,294)
( 97,295)( 98,296)( 99,297)(100,331)(101,332)(102,333)(103,334)(104,335)
(105,336)(106,337)(107,338)(108,339)(109,340)(110,341)(111,342)(112,343)
(113,344)(114,345)(115,346)(116,347)(117,348)(118,349)(119,350)(120,351)
(121,352)(122,353)(123,354)(124,355)(125,356)(126,357)(127,358)(128,359)
(129,360)(130,361)(131,362)(132,363)(133,298)(134,299)(135,300)(136,301)
(137,302)(138,303)(139,304)(140,305)(141,306)(142,307)(143,308)(144,309)
(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)(152,317)
(153,318)(154,319)(155,320)(156,321)(157,322)(158,323)(159,324)(160,325)
(161,326)(162,327)(163,328)(164,329)(165,330)(166,364)(167,365)(168,366)
(169,367)(170,368)(171,369)(172,370)(173,371)(174,372)(175,373)(176,374)
(177,375)(178,376)(179,377)(180,378)(181,379)(182,380)(183,381)(184,382)
(185,383)(186,384)(187,385)(188,386)(189,387)(190,388)(191,389)(192,390)
(193,391)(194,392)(195,393)(196,394)(197,395)(198,396);;
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,
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*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, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 12, 23)( 13, 33)
( 14, 32)( 15, 31)( 16, 30)( 17, 29)( 18, 28)( 19, 27)( 20, 26)( 21, 25)
( 22, 24)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 45, 56)( 46, 66)
( 47, 65)( 48, 64)( 49, 63)( 50, 62)( 51, 61)( 52, 60)( 53, 59)( 54, 58)
( 55, 57)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 78, 89)( 79, 99)
( 80, 98)( 81, 97)( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)
( 88, 90)(101,110)(102,109)(103,108)(104,107)(105,106)(111,122)(112,132)
(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)
(121,123)(134,143)(135,142)(136,141)(137,140)(138,139)(144,155)(145,165)
(146,164)(147,163)(148,162)(149,161)(150,160)(151,159)(152,158)(153,157)
(154,156)(167,176)(168,175)(169,174)(170,173)(171,172)(177,188)(178,198)
(179,197)(180,196)(181,195)(182,194)(183,193)(184,192)(185,191)(186,190)
(187,189)(200,209)(201,208)(202,207)(203,206)(204,205)(210,221)(211,231)
(212,230)(213,229)(214,228)(215,227)(216,226)(217,225)(218,224)(219,223)
(220,222)(233,242)(234,241)(235,240)(236,239)(237,238)(243,254)(244,264)
(245,263)(246,262)(247,261)(248,260)(249,259)(250,258)(251,257)(252,256)
(253,255)(266,275)(267,274)(268,273)(269,272)(270,271)(276,287)(277,297)
(278,296)(279,295)(280,294)(281,293)(282,292)(283,291)(284,290)(285,289)
(286,288)(299,308)(300,307)(301,306)(302,305)(303,304)(309,320)(310,330)
(311,329)(312,328)(313,327)(314,326)(315,325)(316,324)(317,323)(318,322)
(319,321)(332,341)(333,340)(334,339)(335,338)(336,337)(342,353)(343,363)
(344,362)(345,361)(346,360)(347,359)(348,358)(349,357)(350,356)(351,355)
(352,354)(365,374)(366,373)(367,372)(368,371)(369,370)(375,386)(376,396)
(377,395)(378,394)(379,393)(380,392)(381,391)(382,390)(383,389)(384,388)
(385,387);
s1 := Sym(396)!( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)
( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 23, 24)( 25, 33)( 26, 32)( 27, 31)
( 28, 30)( 34, 79)( 35, 78)( 36, 88)( 37, 87)( 38, 86)( 39, 85)( 40, 84)
( 41, 83)( 42, 82)( 43, 81)( 44, 80)( 45, 68)( 46, 67)( 47, 77)( 48, 76)
( 49, 75)( 50, 74)( 51, 73)( 52, 72)( 53, 71)( 54, 70)( 55, 69)( 56, 90)
( 57, 89)( 58, 99)( 59, 98)( 60, 97)( 61, 96)( 62, 95)( 63, 94)( 64, 93)
( 65, 92)( 66, 91)(100,112)(101,111)(102,121)(103,120)(104,119)(105,118)
(106,117)(107,116)(108,115)(109,114)(110,113)(122,123)(124,132)(125,131)
(126,130)(127,129)(133,178)(134,177)(135,187)(136,186)(137,185)(138,184)
(139,183)(140,182)(141,181)(142,180)(143,179)(144,167)(145,166)(146,176)
(147,175)(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)
(155,189)(156,188)(157,198)(158,197)(159,196)(160,195)(161,194)(162,193)
(163,192)(164,191)(165,190)(199,310)(200,309)(201,319)(202,318)(203,317)
(204,316)(205,315)(206,314)(207,313)(208,312)(209,311)(210,299)(211,298)
(212,308)(213,307)(214,306)(215,305)(216,304)(217,303)(218,302)(219,301)
(220,300)(221,321)(222,320)(223,330)(224,329)(225,328)(226,327)(227,326)
(228,325)(229,324)(230,323)(231,322)(232,376)(233,375)(234,385)(235,384)
(236,383)(237,382)(238,381)(239,380)(240,379)(241,378)(242,377)(243,365)
(244,364)(245,374)(246,373)(247,372)(248,371)(249,370)(250,369)(251,368)
(252,367)(253,366)(254,387)(255,386)(256,396)(257,395)(258,394)(259,393)
(260,392)(261,391)(262,390)(263,389)(264,388)(265,343)(266,342)(267,352)
(268,351)(269,350)(270,349)(271,348)(272,347)(273,346)(274,345)(275,344)
(276,332)(277,331)(278,341)(279,340)(280,339)(281,338)(282,337)(283,336)
(284,335)(285,334)(286,333)(287,354)(288,353)(289,363)(290,362)(291,361)
(292,360)(293,359)(294,358)(295,357)(296,356)(297,355);
s2 := Sym(396)!( 1,232)( 2,233)( 3,234)( 4,235)( 5,236)( 6,237)( 7,238)
( 8,239)( 9,240)( 10,241)( 11,242)( 12,243)( 13,244)( 14,245)( 15,246)
( 16,247)( 17,248)( 18,249)( 19,250)( 20,251)( 21,252)( 22,253)( 23,254)
( 24,255)( 25,256)( 26,257)( 27,258)( 28,259)( 29,260)( 30,261)( 31,262)
( 32,263)( 33,264)( 34,199)( 35,200)( 36,201)( 37,202)( 38,203)( 39,204)
( 40,205)( 41,206)( 42,207)( 43,208)( 44,209)( 45,210)( 46,211)( 47,212)
( 48,213)( 49,214)( 50,215)( 51,216)( 52,217)( 53,218)( 54,219)( 55,220)
( 56,221)( 57,222)( 58,223)( 59,224)( 60,225)( 61,226)( 62,227)( 63,228)
( 64,229)( 65,230)( 66,231)( 67,265)( 68,266)( 69,267)( 70,268)( 71,269)
( 72,270)( 73,271)( 74,272)( 75,273)( 76,274)( 77,275)( 78,276)( 79,277)
( 80,278)( 81,279)( 82,280)( 83,281)( 84,282)( 85,283)( 86,284)( 87,285)
( 88,286)( 89,287)( 90,288)( 91,289)( 92,290)( 93,291)( 94,292)( 95,293)
( 96,294)( 97,295)( 98,296)( 99,297)(100,331)(101,332)(102,333)(103,334)
(104,335)(105,336)(106,337)(107,338)(108,339)(109,340)(110,341)(111,342)
(112,343)(113,344)(114,345)(115,346)(116,347)(117,348)(118,349)(119,350)
(120,351)(121,352)(122,353)(123,354)(124,355)(125,356)(126,357)(127,358)
(128,359)(129,360)(130,361)(131,362)(132,363)(133,298)(134,299)(135,300)
(136,301)(137,302)(138,303)(139,304)(140,305)(141,306)(142,307)(143,308)
(144,309)(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)
(152,317)(153,318)(154,319)(155,320)(156,321)(157,322)(158,323)(159,324)
(160,325)(161,326)(162,327)(163,328)(164,329)(165,330)(166,364)(167,365)
(168,366)(169,367)(170,368)(171,369)(172,370)(173,371)(174,372)(175,373)
(176,374)(177,375)(178,376)(179,377)(180,378)(181,379)(182,380)(183,381)
(184,382)(185,383)(186,384)(187,385)(188,386)(189,387)(190,388)(191,389)
(192,390)(193,391)(194,392)(195,393)(196,394)(197,395)(198,396);
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,
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*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