Polytope of Type {396}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {396}*792
Also Known As : 396-gon, {396}. if this polytope has another name.
Group : SmallGroup(792,25)
Rank : 2
Schlafli Type : {396}
Number of vertices, edges, etc : 396, 396
Order of s0s1 : 396
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{396,2} of size 1584
Vertex Figure Of :
{2,396} of size 1584
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {198}*396
3-fold quotients : {132}*264
4-fold quotients : {99}*198
6-fold quotients : {66}*132
9-fold quotients : {44}*88
11-fold quotients : {36}*72
12-fold quotients : {33}*66
18-fold quotients : {22}*44
22-fold quotients : {18}*36
33-fold quotients : {12}*24
36-fold quotients : {11}*22
44-fold quotients : {9}*18
66-fold quotients : {6}*12
99-fold quotients : {4}*8
132-fold quotients : {3}*6
198-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {792}*1584
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 31)( 5, 33)( 6, 32)( 7, 28)( 8, 30)( 9, 29)( 10, 25)
( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 16, 19)( 17, 21)( 18, 20)
( 34, 69)( 35, 68)( 36, 67)( 37, 99)( 38, 98)( 39, 97)( 40, 96)( 41, 95)
( 42, 94)( 43, 93)( 44, 92)( 45, 91)( 46, 90)( 47, 89)( 48, 88)( 49, 87)
( 50, 86)( 51, 85)( 52, 84)( 53, 83)( 54, 82)( 55, 81)( 56, 80)( 57, 79)
( 58, 78)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 64, 72)( 65, 71)
( 66, 70)(101,102)(103,130)(104,132)(105,131)(106,127)(107,129)(108,128)
(109,124)(110,126)(111,125)(112,121)(113,123)(114,122)(115,118)(116,120)
(117,119)(133,168)(134,167)(135,166)(136,198)(137,197)(138,196)(139,195)
(140,194)(141,193)(142,192)(143,191)(144,190)(145,189)(146,188)(147,187)
(148,186)(149,185)(150,184)(151,183)(152,182)(153,181)(154,180)(155,179)
(156,178)(157,177)(158,176)(159,175)(160,174)(161,173)(162,172)(163,171)
(164,170)(165,169)(199,298)(200,300)(201,299)(202,328)(203,330)(204,329)
(205,325)(206,327)(207,326)(208,322)(209,324)(210,323)(211,319)(212,321)
(213,320)(214,316)(215,318)(216,317)(217,313)(218,315)(219,314)(220,310)
(221,312)(222,311)(223,307)(224,309)(225,308)(226,304)(227,306)(228,305)
(229,301)(230,303)(231,302)(232,366)(233,365)(234,364)(235,396)(236,395)
(237,394)(238,393)(239,392)(240,391)(241,390)(242,389)(243,388)(244,387)
(245,386)(246,385)(247,384)(248,383)(249,382)(250,381)(251,380)(252,379)
(253,378)(254,377)(255,376)(256,375)(257,374)(258,373)(259,372)(260,371)
(261,370)(262,369)(263,368)(264,367)(265,333)(266,332)(267,331)(268,363)
(269,362)(270,361)(271,360)(272,359)(273,358)(274,357)(275,356)(276,355)
(277,354)(278,353)(279,352)(280,351)(281,350)(282,349)(283,348)(284,347)
(285,346)(286,345)(287,344)(288,343)(289,342)(290,341)(291,340)(292,339)
(293,338)(294,337)(295,336)(296,335)(297,334);;
s1 := ( 1,235)( 2,237)( 3,236)( 4,232)( 5,234)( 6,233)( 7,262)( 8,264)
( 9,263)( 10,259)( 11,261)( 12,260)( 13,256)( 14,258)( 15,257)( 16,253)
( 17,255)( 18,254)( 19,250)( 20,252)( 21,251)( 22,247)( 23,249)( 24,248)
( 25,244)( 26,246)( 27,245)( 28,241)( 29,243)( 30,242)( 31,238)( 32,240)
( 33,239)( 34,202)( 35,204)( 36,203)( 37,199)( 38,201)( 39,200)( 40,229)
( 41,231)( 42,230)( 43,226)( 44,228)( 45,227)( 46,223)( 47,225)( 48,224)
( 49,220)( 50,222)( 51,221)( 52,217)( 53,219)( 54,218)( 55,214)( 56,216)
( 57,215)( 58,211)( 59,213)( 60,212)( 61,208)( 62,210)( 63,209)( 64,205)
( 65,207)( 66,206)( 67,270)( 68,269)( 69,268)( 70,267)( 71,266)( 72,265)
( 73,297)( 74,296)( 75,295)( 76,294)( 77,293)( 78,292)( 79,291)( 80,290)
( 81,289)( 82,288)( 83,287)( 84,286)( 85,285)( 86,284)( 87,283)( 88,282)
( 89,281)( 90,280)( 91,279)( 92,278)( 93,277)( 94,276)( 95,275)( 96,274)
( 97,273)( 98,272)( 99,271)(100,334)(101,336)(102,335)(103,331)(104,333)
(105,332)(106,361)(107,363)(108,362)(109,358)(110,360)(111,359)(112,355)
(113,357)(114,356)(115,352)(116,354)(117,353)(118,349)(119,351)(120,350)
(121,346)(122,348)(123,347)(124,343)(125,345)(126,344)(127,340)(128,342)
(129,341)(130,337)(131,339)(132,338)(133,301)(134,303)(135,302)(136,298)
(137,300)(138,299)(139,328)(140,330)(141,329)(142,325)(143,327)(144,326)
(145,322)(146,324)(147,323)(148,319)(149,321)(150,320)(151,316)(152,318)
(153,317)(154,313)(155,315)(156,314)(157,310)(158,312)(159,311)(160,307)
(161,309)(162,308)(163,304)(164,306)(165,305)(166,369)(167,368)(168,367)
(169,366)(170,365)(171,364)(172,396)(173,395)(174,394)(175,393)(176,392)
(177,391)(178,390)(179,389)(180,388)(181,387)(182,386)(183,385)(184,384)
(185,383)(186,382)(187,381)(188,380)(189,379)(190,378)(191,377)(192,376)
(193,375)(194,374)(195,373)(196,372)(197,371)(198,370);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*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*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*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*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*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*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(396)!( 2, 3)( 4, 31)( 5, 33)( 6, 32)( 7, 28)( 8, 30)( 9, 29)
( 10, 25)( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 16, 19)( 17, 21)
( 18, 20)( 34, 69)( 35, 68)( 36, 67)( 37, 99)( 38, 98)( 39, 97)( 40, 96)
( 41, 95)( 42, 94)( 43, 93)( 44, 92)( 45, 91)( 46, 90)( 47, 89)( 48, 88)
( 49, 87)( 50, 86)( 51, 85)( 52, 84)( 53, 83)( 54, 82)( 55, 81)( 56, 80)
( 57, 79)( 58, 78)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 64, 72)
( 65, 71)( 66, 70)(101,102)(103,130)(104,132)(105,131)(106,127)(107,129)
(108,128)(109,124)(110,126)(111,125)(112,121)(113,123)(114,122)(115,118)
(116,120)(117,119)(133,168)(134,167)(135,166)(136,198)(137,197)(138,196)
(139,195)(140,194)(141,193)(142,192)(143,191)(144,190)(145,189)(146,188)
(147,187)(148,186)(149,185)(150,184)(151,183)(152,182)(153,181)(154,180)
(155,179)(156,178)(157,177)(158,176)(159,175)(160,174)(161,173)(162,172)
(163,171)(164,170)(165,169)(199,298)(200,300)(201,299)(202,328)(203,330)
(204,329)(205,325)(206,327)(207,326)(208,322)(209,324)(210,323)(211,319)
(212,321)(213,320)(214,316)(215,318)(216,317)(217,313)(218,315)(219,314)
(220,310)(221,312)(222,311)(223,307)(224,309)(225,308)(226,304)(227,306)
(228,305)(229,301)(230,303)(231,302)(232,366)(233,365)(234,364)(235,396)
(236,395)(237,394)(238,393)(239,392)(240,391)(241,390)(242,389)(243,388)
(244,387)(245,386)(246,385)(247,384)(248,383)(249,382)(250,381)(251,380)
(252,379)(253,378)(254,377)(255,376)(256,375)(257,374)(258,373)(259,372)
(260,371)(261,370)(262,369)(263,368)(264,367)(265,333)(266,332)(267,331)
(268,363)(269,362)(270,361)(271,360)(272,359)(273,358)(274,357)(275,356)
(276,355)(277,354)(278,353)(279,352)(280,351)(281,350)(282,349)(283,348)
(284,347)(285,346)(286,345)(287,344)(288,343)(289,342)(290,341)(291,340)
(292,339)(293,338)(294,337)(295,336)(296,335)(297,334);
s1 := Sym(396)!( 1,235)( 2,237)( 3,236)( 4,232)( 5,234)( 6,233)( 7,262)
( 8,264)( 9,263)( 10,259)( 11,261)( 12,260)( 13,256)( 14,258)( 15,257)
( 16,253)( 17,255)( 18,254)( 19,250)( 20,252)( 21,251)( 22,247)( 23,249)
( 24,248)( 25,244)( 26,246)( 27,245)( 28,241)( 29,243)( 30,242)( 31,238)
( 32,240)( 33,239)( 34,202)( 35,204)( 36,203)( 37,199)( 38,201)( 39,200)
( 40,229)( 41,231)( 42,230)( 43,226)( 44,228)( 45,227)( 46,223)( 47,225)
( 48,224)( 49,220)( 50,222)( 51,221)( 52,217)( 53,219)( 54,218)( 55,214)
( 56,216)( 57,215)( 58,211)( 59,213)( 60,212)( 61,208)( 62,210)( 63,209)
( 64,205)( 65,207)( 66,206)( 67,270)( 68,269)( 69,268)( 70,267)( 71,266)
( 72,265)( 73,297)( 74,296)( 75,295)( 76,294)( 77,293)( 78,292)( 79,291)
( 80,290)( 81,289)( 82,288)( 83,287)( 84,286)( 85,285)( 86,284)( 87,283)
( 88,282)( 89,281)( 90,280)( 91,279)( 92,278)( 93,277)( 94,276)( 95,275)
( 96,274)( 97,273)( 98,272)( 99,271)(100,334)(101,336)(102,335)(103,331)
(104,333)(105,332)(106,361)(107,363)(108,362)(109,358)(110,360)(111,359)
(112,355)(113,357)(114,356)(115,352)(116,354)(117,353)(118,349)(119,351)
(120,350)(121,346)(122,348)(123,347)(124,343)(125,345)(126,344)(127,340)
(128,342)(129,341)(130,337)(131,339)(132,338)(133,301)(134,303)(135,302)
(136,298)(137,300)(138,299)(139,328)(140,330)(141,329)(142,325)(143,327)
(144,326)(145,322)(146,324)(147,323)(148,319)(149,321)(150,320)(151,316)
(152,318)(153,317)(154,313)(155,315)(156,314)(157,310)(158,312)(159,311)
(160,307)(161,309)(162,308)(163,304)(164,306)(165,305)(166,369)(167,368)
(168,367)(169,366)(170,365)(171,364)(172,396)(173,395)(174,394)(175,393)
(176,392)(177,391)(178,390)(179,389)(180,388)(181,387)(182,386)(183,385)
(184,384)(185,383)(186,382)(187,381)(188,380)(189,379)(190,378)(191,377)
(192,376)(193,375)(194,374)(195,373)(196,372)(197,371)(198,370);
poly := sub<Sym(396)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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*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*s0*s1 >;
References : None.
to this polytope