Polytope of Type {392}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {392}*784
Also Known As : 392-gon, {392}. if this polytope has another name.
Group : SmallGroup(784,7)
Rank : 2
Schlafli Type : {392}
Number of vertices, edges, etc : 392, 392
Order of s₀s₁ : 392
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {392,2} of size 1568
Vertex Figure Of :
   {2,392} of size 1568
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {196}*392
   4-fold quotients : {98}*196
   7-fold quotients : {56}*112
   8-fold quotients : {49}*98
   14-fold quotients : {28}*56
   28-fold quotients : {14}*28
   49-fold quotients : {8}*16
   56-fold quotients : {7}*14
   98-fold quotients : {4}*8
   196-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {784}*1568
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope