Polytope of Type {376}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {376}*752
Also Known As : 376-gon, {376}. if this polytope has another name.
Group : SmallGroup(752,6)
Rank : 2
Schlafli Type : {376}
Number of vertices, edges, etc : 376, 376
Order of s₀s₁ : 376
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {376,2} of size 1504
Vertex Figure Of :
   {2,376} of size 1504
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {188}*376
   4-fold quotients : {94}*188
   8-fold quotients : {47}*94
   47-fold quotients : {8}*16
   94-fold quotients : {4}*8
   188-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {752}*1504
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope