Polytope of Type {388}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {388}*776
Also Known As : 388-gon, {388}. if this polytope has another name.
Group : SmallGroup(776,6)
Rank : 2
Schlafli Type : {388}
Number of vertices, edges, etc : 388, 388
Order of s₀s₁ : 388
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {388,2} of size 1552
Vertex Figure Of :
   {2,388} of size 1552
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {194}*388
   4-fold quotients : {97}*194
   97-fold quotients : {4}*8
   194-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {776}*1552
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope