Polytope of Type {2,392}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,392}*1568
if this polytope has a name.
Group : SmallGroup(1568,99)
Rank : 3
Schlafli Type : {2,392}
Number of vertices, edges, etc : 2, 392, 392
Order of s₀s₁s₂ : 392
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 : {2,196}*784
   4-fold quotients : {2,98}*392
   7-fold quotients : {2,56}*224
   8-fold quotients : {2,49}*196
   14-fold quotients : {2,28}*112
   28-fold quotients : {2,14}*56
   49-fold quotients : {2,8}*32
   56-fold quotients : {2,7}*28
   98-fold quotients : {2,4}*16
   196-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope