Polytope of Type {8,98}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,98}*1568
Also Known As : {8,98|2}. if this polytope has another name.
Group : SmallGroup(1568,105)
Rank : 3
Schlafli Type : {8,98}
Number of vertices, edges, etc : 8, 392, 98
Order of s₀s₁s₂ : 392
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 : {4,98}*784
   4-fold quotients : {2,98}*392
   7-fold quotients : {8,14}*224
   8-fold quotients : {2,49}*196
   14-fold quotients : {4,14}*112
   28-fold quotients : {2,14}*56
   49-fold quotients : {8,2}*32
   56-fold quotients : {2,7}*28
   98-fold quotients : {4,2}*16
   196-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope