Polytope of Type {2,396}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,396}*1584
if this polytope has a name.
Group : SmallGroup(1584,154)
Rank : 3
Schlafli Type : {2,396}
Number of vertices, edges, etc : 2, 396, 396
Order of s₀s₁s₂ : 396
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   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 : {2,198}*792
   3-fold quotients : {2,132}*528
   4-fold quotients : {2,99}*396
   6-fold quotients : {2,66}*264
   9-fold quotients : {2,44}*176
   11-fold quotients : {2,36}*144
   12-fold quotients : {2,33}*132
   18-fold quotients : {2,22}*88
   22-fold quotients : {2,18}*72
   33-fold quotients : {2,12}*48
   36-fold quotients : {2,11}*44
   44-fold quotients : {2,9}*36
   66-fold quotients : {2,6}*24
   99-fold quotients : {2,4}*16
   132-fold quotients : {2,3}*12
   198-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  5)(  6, 33)(  7, 35)(  8, 34)(  9, 30)( 10, 32)( 11, 31)( 12, 27)
( 13, 29)( 14, 28)( 15, 24)( 16, 26)( 17, 25)( 18, 21)( 19, 23)( 20, 22)
( 36, 71)( 37, 70)( 38, 69)( 39,101)( 40,100)( 41, 99)( 42, 98)( 43, 97)
( 44, 96)( 45, 95)( 46, 94)( 47, 93)( 48, 92)( 49, 91)( 50, 90)( 51, 89)
( 52, 88)( 53, 87)( 54, 86)( 55, 85)( 56, 84)( 57, 83)( 58, 82)( 59, 81)
( 60, 80)( 61, 79)( 62, 78)( 63, 77)( 64, 76)( 65, 75)( 66, 74)( 67, 73)
( 68, 72)(103,104)(105,132)(106,134)(107,133)(108,129)(109,131)(110,130)
(111,126)(112,128)(113,127)(114,123)(115,125)(116,124)(117,120)(118,122)
(119,121)(135,170)(136,169)(137,168)(138,200)(139,199)(140,198)(141,197)
(142,196)(143,195)(144,194)(145,193)(146,192)(147,191)(148,190)(149,189)
(150,188)(151,187)(152,186)(153,185)(154,184)(155,183)(156,182)(157,181)
(158,180)(159,179)(160,178)(161,177)(162,176)(163,175)(164,174)(165,173)
(166,172)(167,171)(201,300)(202,302)(203,301)(204,330)(205,332)(206,331)
(207,327)(208,329)(209,328)(210,324)(211,326)(212,325)(213,321)(214,323)
(215,322)(216,318)(217,320)(218,319)(219,315)(220,317)(221,316)(222,312)
(223,314)(224,313)(225,309)(226,311)(227,310)(228,306)(229,308)(230,307)
(231,303)(232,305)(233,304)(234,368)(235,367)(236,366)(237,398)(238,397)
(239,396)(240,395)(241,394)(242,393)(243,392)(244,391)(245,390)(246,389)
(247,388)(248,387)(249,386)(250,385)(251,384)(252,383)(253,382)(254,381)
(255,380)(256,379)(257,378)(258,377)(259,376)(260,375)(261,374)(262,373)
(263,372)(264,371)(265,370)(266,369)(267,335)(268,334)(269,333)(270,365)
(271,364)(272,363)(273,362)(274,361)(275,360)(276,359)(277,358)(278,357)
(279,356)(280,355)(281,354)(282,353)(283,352)(284,351)(285,350)(286,349)
(287,348)(288,347)(289,346)(290,345)(291,344)(292,343)(293,342)(294,341)
(295,340)(296,339)(297,338)(298,337)(299,336);;
s2 := (  3,237)(  4,239)(  5,238)(  6,234)(  7,236)(  8,235)(  9,264)( 10,266)
( 11,265)( 12,261)( 13,263)( 14,262)( 15,258)( 16,260)( 17,259)( 18,255)
( 19,257)( 20,256)( 21,252)( 22,254)( 23,253)( 24,249)( 25,251)( 26,250)
( 27,246)( 28,248)( 29,247)( 30,243)( 31,245)( 32,244)( 33,240)( 34,242)
( 35,241)( 36,204)( 37,206)( 38,205)( 39,201)( 40,203)( 41,202)( 42,231)
( 43,233)( 44,232)( 45,228)( 46,230)( 47,229)( 48,225)( 49,227)( 50,226)
( 51,222)( 52,224)( 53,223)( 54,219)( 55,221)( 56,220)( 57,216)( 58,218)
( 59,217)( 60,213)( 61,215)( 62,214)( 63,210)( 64,212)( 65,211)( 66,207)
( 67,209)( 68,208)( 69,272)( 70,271)( 71,270)( 72,269)( 73,268)( 74,267)
( 75,299)( 76,298)( 77,297)( 78,296)( 79,295)( 80,294)( 81,293)( 82,292)
( 83,291)( 84,290)( 85,289)( 86,288)( 87,287)( 88,286)( 89,285)( 90,284)
( 91,283)( 92,282)( 93,281)( 94,280)( 95,279)( 96,278)( 97,277)( 98,276)
( 99,275)(100,274)(101,273)(102,336)(103,338)(104,337)(105,333)(106,335)
(107,334)(108,363)(109,365)(110,364)(111,360)(112,362)(113,361)(114,357)
(115,359)(116,358)(117,354)(118,356)(119,355)(120,351)(121,353)(122,352)
(123,348)(124,350)(125,349)(126,345)(127,347)(128,346)(129,342)(130,344)
(131,343)(132,339)(133,341)(134,340)(135,303)(136,305)(137,304)(138,300)
(139,302)(140,301)(141,330)(142,332)(143,331)(144,327)(145,329)(146,328)
(147,324)(148,326)(149,325)(150,321)(151,323)(152,322)(153,318)(154,320)
(155,319)(156,315)(157,317)(158,316)(159,312)(160,314)(161,313)(162,309)
(163,311)(164,310)(165,306)(166,308)(167,307)(168,371)(169,370)(170,369)
(171,368)(172,367)(173,366)(174,398)(175,397)(176,396)(177,395)(178,394)
(179,393)(180,392)(181,391)(182,390)(183,389)(184,388)(185,387)(186,386)
(187,385)(188,384)(189,383)(190,382)(191,381)(192,380)(193,379)(194,378)
(195,377)(196,376)(197,375)(198,374)(199,373)(200,372);;
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*s1*s0*s1, s0*s2*s0*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*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*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*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*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*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*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*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*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*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(398)!(1,2);
s1 := Sym(398)!(  4,  5)(  6, 33)(  7, 35)(  8, 34)(  9, 30)( 10, 32)( 11, 31)
( 12, 27)( 13, 29)( 14, 28)( 15, 24)( 16, 26)( 17, 25)( 18, 21)( 19, 23)
( 20, 22)( 36, 71)( 37, 70)( 38, 69)( 39,101)( 40,100)( 41, 99)( 42, 98)
( 43, 97)( 44, 96)( 45, 95)( 46, 94)( 47, 93)( 48, 92)( 49, 91)( 50, 90)
( 51, 89)( 52, 88)( 53, 87)( 54, 86)( 55, 85)( 56, 84)( 57, 83)( 58, 82)
( 59, 81)( 60, 80)( 61, 79)( 62, 78)( 63, 77)( 64, 76)( 65, 75)( 66, 74)
( 67, 73)( 68, 72)(103,104)(105,132)(106,134)(107,133)(108,129)(109,131)
(110,130)(111,126)(112,128)(113,127)(114,123)(115,125)(116,124)(117,120)
(118,122)(119,121)(135,170)(136,169)(137,168)(138,200)(139,199)(140,198)
(141,197)(142,196)(143,195)(144,194)(145,193)(146,192)(147,191)(148,190)
(149,189)(150,188)(151,187)(152,186)(153,185)(154,184)(155,183)(156,182)
(157,181)(158,180)(159,179)(160,178)(161,177)(162,176)(163,175)(164,174)
(165,173)(166,172)(167,171)(201,300)(202,302)(203,301)(204,330)(205,332)
(206,331)(207,327)(208,329)(209,328)(210,324)(211,326)(212,325)(213,321)
(214,323)(215,322)(216,318)(217,320)(218,319)(219,315)(220,317)(221,316)
(222,312)(223,314)(224,313)(225,309)(226,311)(227,310)(228,306)(229,308)
(230,307)(231,303)(232,305)(233,304)(234,368)(235,367)(236,366)(237,398)
(238,397)(239,396)(240,395)(241,394)(242,393)(243,392)(244,391)(245,390)
(246,389)(247,388)(248,387)(249,386)(250,385)(251,384)(252,383)(253,382)
(254,381)(255,380)(256,379)(257,378)(258,377)(259,376)(260,375)(261,374)
(262,373)(263,372)(264,371)(265,370)(266,369)(267,335)(268,334)(269,333)
(270,365)(271,364)(272,363)(273,362)(274,361)(275,360)(276,359)(277,358)
(278,357)(279,356)(280,355)(281,354)(282,353)(283,352)(284,351)(285,350)
(286,349)(287,348)(288,347)(289,346)(290,345)(291,344)(292,343)(293,342)
(294,341)(295,340)(296,339)(297,338)(298,337)(299,336);
s2 := Sym(398)!(  3,237)(  4,239)(  5,238)(  6,234)(  7,236)(  8,235)(  9,264)
( 10,266)( 11,265)( 12,261)( 13,263)( 14,262)( 15,258)( 16,260)( 17,259)
( 18,255)( 19,257)( 20,256)( 21,252)( 22,254)( 23,253)( 24,249)( 25,251)
( 26,250)( 27,246)( 28,248)( 29,247)( 30,243)( 31,245)( 32,244)( 33,240)
( 34,242)( 35,241)( 36,204)( 37,206)( 38,205)( 39,201)( 40,203)( 41,202)
( 42,231)( 43,233)( 44,232)( 45,228)( 46,230)( 47,229)( 48,225)( 49,227)
( 50,226)( 51,222)( 52,224)( 53,223)( 54,219)( 55,221)( 56,220)( 57,216)
( 58,218)( 59,217)( 60,213)( 61,215)( 62,214)( 63,210)( 64,212)( 65,211)
( 66,207)( 67,209)( 68,208)( 69,272)( 70,271)( 71,270)( 72,269)( 73,268)
( 74,267)( 75,299)( 76,298)( 77,297)( 78,296)( 79,295)( 80,294)( 81,293)
( 82,292)( 83,291)( 84,290)( 85,289)( 86,288)( 87,287)( 88,286)( 89,285)
( 90,284)( 91,283)( 92,282)( 93,281)( 94,280)( 95,279)( 96,278)( 97,277)
( 98,276)( 99,275)(100,274)(101,273)(102,336)(103,338)(104,337)(105,333)
(106,335)(107,334)(108,363)(109,365)(110,364)(111,360)(112,362)(113,361)
(114,357)(115,359)(116,358)(117,354)(118,356)(119,355)(120,351)(121,353)
(122,352)(123,348)(124,350)(125,349)(126,345)(127,347)(128,346)(129,342)
(130,344)(131,343)(132,339)(133,341)(134,340)(135,303)(136,305)(137,304)
(138,300)(139,302)(140,301)(141,330)(142,332)(143,331)(144,327)(145,329)
(146,328)(147,324)(148,326)(149,325)(150,321)(151,323)(152,322)(153,318)
(154,320)(155,319)(156,315)(157,317)(158,316)(159,312)(160,314)(161,313)
(162,309)(163,311)(164,310)(165,306)(166,308)(167,307)(168,371)(169,370)
(170,369)(171,368)(172,367)(173,366)(174,398)(175,397)(176,396)(177,395)
(178,394)(179,393)(180,392)(181,391)(182,390)(183,389)(184,388)(185,387)
(186,386)(187,385)(188,384)(189,383)(190,382)(191,381)(192,380)(193,379)
(194,378)(195,377)(196,376)(197,375)(198,374)(199,373)(200,372);
poly := sub<Sym(398)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*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*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*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*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*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*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*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*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*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*s1*s2 >;

to this polytope