Polytope of Type {4,99}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,99}*792
if this polytope has a name.
Group : SmallGroup(792,38)
Rank : 3
Schlafli Type : {4,99}
Number of vertices, edges, etc : 4, 198, 99
Order of s0s1s2 : 99
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,99,2} of size 1584
Vertex Figure Of :
{2,4,99} of size 1584
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {4,33}*264
11-fold quotients : {4,9}*72
33-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,99}*1584, {4,198}*1584b, {4,198}*1584c
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396);;
s1 := ( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13,121)( 14,123)( 15,122)
( 16,124)( 17,129)( 18,131)( 19,130)( 20,132)( 21,125)( 22,127)( 23,126)
( 24,128)( 25,109)( 26,111)( 27,110)( 28,112)( 29,117)( 30,119)( 31,118)
( 32,120)( 33,113)( 34,115)( 35,114)( 36,116)( 37, 97)( 38, 99)( 39, 98)
( 40,100)( 41,105)( 42,107)( 43,106)( 44,108)( 45,101)( 46,103)( 47,102)
( 48,104)( 49, 85)( 50, 87)( 51, 86)( 52, 88)( 53, 93)( 54, 95)( 55, 94)
( 56, 96)( 57, 89)( 58, 91)( 59, 90)( 60, 92)( 61, 73)( 62, 75)( 63, 74)
( 64, 76)( 65, 81)( 66, 83)( 67, 82)( 68, 84)( 69, 77)( 70, 79)( 71, 78)
( 72, 80)(133,269)(134,271)(135,270)(136,272)(137,265)(138,267)(139,266)
(140,268)(141,273)(142,275)(143,274)(144,276)(145,389)(146,391)(147,390)
(148,392)(149,385)(150,387)(151,386)(152,388)(153,393)(154,395)(155,394)
(156,396)(157,377)(158,379)(159,378)(160,380)(161,373)(162,375)(163,374)
(164,376)(165,381)(166,383)(167,382)(168,384)(169,365)(170,367)(171,366)
(172,368)(173,361)(174,363)(175,362)(176,364)(177,369)(178,371)(179,370)
(180,372)(181,353)(182,355)(183,354)(184,356)(185,349)(186,351)(187,350)
(188,352)(189,357)(190,359)(191,358)(192,360)(193,341)(194,343)(195,342)
(196,344)(197,337)(198,339)(199,338)(200,340)(201,345)(202,347)(203,346)
(204,348)(205,329)(206,331)(207,330)(208,332)(209,325)(210,327)(211,326)
(212,328)(213,333)(214,335)(215,334)(216,336)(217,317)(218,319)(219,318)
(220,320)(221,313)(222,315)(223,314)(224,316)(225,321)(226,323)(227,322)
(228,324)(229,305)(230,307)(231,306)(232,308)(233,301)(234,303)(235,302)
(236,304)(237,309)(238,311)(239,310)(240,312)(241,293)(242,295)(243,294)
(244,296)(245,289)(246,291)(247,290)(248,292)(249,297)(250,299)(251,298)
(252,300)(253,281)(254,283)(255,282)(256,284)(257,277)(258,279)(259,278)
(260,280)(261,285)(262,287)(263,286)(264,288);;
s2 := ( 1,277)( 2,280)( 3,279)( 4,278)( 5,285)( 6,288)( 7,287)( 8,286)
( 9,281)( 10,284)( 11,283)( 12,282)( 13,265)( 14,268)( 15,267)( 16,266)
( 17,273)( 18,276)( 19,275)( 20,274)( 21,269)( 22,272)( 23,271)( 24,270)
( 25,385)( 26,388)( 27,387)( 28,386)( 29,393)( 30,396)( 31,395)( 32,394)
( 33,389)( 34,392)( 35,391)( 36,390)( 37,373)( 38,376)( 39,375)( 40,374)
( 41,381)( 42,384)( 43,383)( 44,382)( 45,377)( 46,380)( 47,379)( 48,378)
( 49,361)( 50,364)( 51,363)( 52,362)( 53,369)( 54,372)( 55,371)( 56,370)
( 57,365)( 58,368)( 59,367)( 60,366)( 61,349)( 62,352)( 63,351)( 64,350)
( 65,357)( 66,360)( 67,359)( 68,358)( 69,353)( 70,356)( 71,355)( 72,354)
( 73,337)( 74,340)( 75,339)( 76,338)( 77,345)( 78,348)( 79,347)( 80,346)
( 81,341)( 82,344)( 83,343)( 84,342)( 85,325)( 86,328)( 87,327)( 88,326)
( 89,333)( 90,336)( 91,335)( 92,334)( 93,329)( 94,332)( 95,331)( 96,330)
( 97,313)( 98,316)( 99,315)(100,314)(101,321)(102,324)(103,323)(104,322)
(105,317)(106,320)(107,319)(108,318)(109,301)(110,304)(111,303)(112,302)
(113,309)(114,312)(115,311)(116,310)(117,305)(118,308)(119,307)(120,306)
(121,289)(122,292)(123,291)(124,290)(125,297)(126,300)(127,299)(128,298)
(129,293)(130,296)(131,295)(132,294)(133,145)(134,148)(135,147)(136,146)
(137,153)(138,156)(139,155)(140,154)(141,149)(142,152)(143,151)(144,150)
(157,253)(158,256)(159,255)(160,254)(161,261)(162,264)(163,263)(164,262)
(165,257)(166,260)(167,259)(168,258)(169,241)(170,244)(171,243)(172,242)
(173,249)(174,252)(175,251)(176,250)(177,245)(178,248)(179,247)(180,246)
(181,229)(182,232)(183,231)(184,230)(185,237)(186,240)(187,239)(188,238)
(189,233)(190,236)(191,235)(192,234)(193,217)(194,220)(195,219)(196,218)
(197,225)(198,228)(199,227)(200,226)(201,221)(202,224)(203,223)(204,222)
(206,208)(209,213)(210,216)(211,215)(212,214);;
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396);
s1 := Sym(396)!( 2, 3)( 5, 9)( 6, 11)( 7, 10)( 8, 12)( 13,121)( 14,123)
( 15,122)( 16,124)( 17,129)( 18,131)( 19,130)( 20,132)( 21,125)( 22,127)
( 23,126)( 24,128)( 25,109)( 26,111)( 27,110)( 28,112)( 29,117)( 30,119)
( 31,118)( 32,120)( 33,113)( 34,115)( 35,114)( 36,116)( 37, 97)( 38, 99)
( 39, 98)( 40,100)( 41,105)( 42,107)( 43,106)( 44,108)( 45,101)( 46,103)
( 47,102)( 48,104)( 49, 85)( 50, 87)( 51, 86)( 52, 88)( 53, 93)( 54, 95)
( 55, 94)( 56, 96)( 57, 89)( 58, 91)( 59, 90)( 60, 92)( 61, 73)( 62, 75)
( 63, 74)( 64, 76)( 65, 81)( 66, 83)( 67, 82)( 68, 84)( 69, 77)( 70, 79)
( 71, 78)( 72, 80)(133,269)(134,271)(135,270)(136,272)(137,265)(138,267)
(139,266)(140,268)(141,273)(142,275)(143,274)(144,276)(145,389)(146,391)
(147,390)(148,392)(149,385)(150,387)(151,386)(152,388)(153,393)(154,395)
(155,394)(156,396)(157,377)(158,379)(159,378)(160,380)(161,373)(162,375)
(163,374)(164,376)(165,381)(166,383)(167,382)(168,384)(169,365)(170,367)
(171,366)(172,368)(173,361)(174,363)(175,362)(176,364)(177,369)(178,371)
(179,370)(180,372)(181,353)(182,355)(183,354)(184,356)(185,349)(186,351)
(187,350)(188,352)(189,357)(190,359)(191,358)(192,360)(193,341)(194,343)
(195,342)(196,344)(197,337)(198,339)(199,338)(200,340)(201,345)(202,347)
(203,346)(204,348)(205,329)(206,331)(207,330)(208,332)(209,325)(210,327)
(211,326)(212,328)(213,333)(214,335)(215,334)(216,336)(217,317)(218,319)
(219,318)(220,320)(221,313)(222,315)(223,314)(224,316)(225,321)(226,323)
(227,322)(228,324)(229,305)(230,307)(231,306)(232,308)(233,301)(234,303)
(235,302)(236,304)(237,309)(238,311)(239,310)(240,312)(241,293)(242,295)
(243,294)(244,296)(245,289)(246,291)(247,290)(248,292)(249,297)(250,299)
(251,298)(252,300)(253,281)(254,283)(255,282)(256,284)(257,277)(258,279)
(259,278)(260,280)(261,285)(262,287)(263,286)(264,288);
s2 := Sym(396)!( 1,277)( 2,280)( 3,279)( 4,278)( 5,285)( 6,288)( 7,287)
( 8,286)( 9,281)( 10,284)( 11,283)( 12,282)( 13,265)( 14,268)( 15,267)
( 16,266)( 17,273)( 18,276)( 19,275)( 20,274)( 21,269)( 22,272)( 23,271)
( 24,270)( 25,385)( 26,388)( 27,387)( 28,386)( 29,393)( 30,396)( 31,395)
( 32,394)( 33,389)( 34,392)( 35,391)( 36,390)( 37,373)( 38,376)( 39,375)
( 40,374)( 41,381)( 42,384)( 43,383)( 44,382)( 45,377)( 46,380)( 47,379)
( 48,378)( 49,361)( 50,364)( 51,363)( 52,362)( 53,369)( 54,372)( 55,371)
( 56,370)( 57,365)( 58,368)( 59,367)( 60,366)( 61,349)( 62,352)( 63,351)
( 64,350)( 65,357)( 66,360)( 67,359)( 68,358)( 69,353)( 70,356)( 71,355)
( 72,354)( 73,337)( 74,340)( 75,339)( 76,338)( 77,345)( 78,348)( 79,347)
( 80,346)( 81,341)( 82,344)( 83,343)( 84,342)( 85,325)( 86,328)( 87,327)
( 88,326)( 89,333)( 90,336)( 91,335)( 92,334)( 93,329)( 94,332)( 95,331)
( 96,330)( 97,313)( 98,316)( 99,315)(100,314)(101,321)(102,324)(103,323)
(104,322)(105,317)(106,320)(107,319)(108,318)(109,301)(110,304)(111,303)
(112,302)(113,309)(114,312)(115,311)(116,310)(117,305)(118,308)(119,307)
(120,306)(121,289)(122,292)(123,291)(124,290)(125,297)(126,300)(127,299)
(128,298)(129,293)(130,296)(131,295)(132,294)(133,145)(134,148)(135,147)
(136,146)(137,153)(138,156)(139,155)(140,154)(141,149)(142,152)(143,151)
(144,150)(157,253)(158,256)(159,255)(160,254)(161,261)(162,264)(163,263)
(164,262)(165,257)(166,260)(167,259)(168,258)(169,241)(170,244)(171,243)
(172,242)(173,249)(174,252)(175,251)(176,250)(177,245)(178,248)(179,247)
(180,246)(181,229)(182,232)(183,231)(184,230)(185,237)(186,240)(187,239)
(188,238)(189,233)(190,236)(191,235)(192,234)(193,217)(194,220)(195,219)
(196,218)(197,225)(198,228)(199,227)(200,226)(201,221)(202,224)(203,223)
(204,222)(206,208)(209,213)(210,216)(211,215)(212,214);
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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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