Polytope of Type {364}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {364}*728
Also Known As : 364-gon, {364}. if this polytope has another name.
Group : SmallGroup(728,26)
Rank : 2
Schlafli Type : {364}
Number of vertices, edges, etc : 364, 364
Order of s0s1 : 364
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{364,2} of size 1456
Vertex Figure Of :
{2,364} of size 1456
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {182}*364
4-fold quotients : {91}*182
7-fold quotients : {52}*104
13-fold quotients : {28}*56
14-fold quotients : {26}*52
26-fold quotients : {14}*28
28-fold quotients : {13}*26
52-fold quotients : {7}*14
91-fold quotients : {4}*8
182-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {728}*1456
Permutation Representation (GAP) :
s0 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 14, 79)( 15, 91)
( 16, 90)( 17, 89)( 18, 88)( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 83)
( 24, 82)( 25, 81)( 26, 80)( 27, 66)( 28, 78)( 29, 77)( 30, 76)( 31, 75)
( 32, 74)( 33, 73)( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)( 39, 67)
( 40, 53)( 41, 65)( 42, 64)( 43, 63)( 44, 62)( 45, 61)( 46, 60)( 47, 59)
( 48, 58)( 49, 57)( 50, 56)( 51, 55)( 52, 54)( 93,104)( 94,103)( 95,102)
( 96,101)( 97,100)( 98, 99)(105,170)(106,182)(107,181)(108,180)(109,179)
(110,178)(111,177)(112,176)(113,175)(114,174)(115,173)(116,172)(117,171)
(118,157)(119,169)(120,168)(121,167)(122,166)(123,165)(124,164)(125,163)
(126,162)(127,161)(128,160)(129,159)(130,158)(131,144)(132,156)(133,155)
(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)
(142,146)(143,145)(183,274)(184,286)(185,285)(186,284)(187,283)(188,282)
(189,281)(190,280)(191,279)(192,278)(193,277)(194,276)(195,275)(196,352)
(197,364)(198,363)(199,362)(200,361)(201,360)(202,359)(203,358)(204,357)
(205,356)(206,355)(207,354)(208,353)(209,339)(210,351)(211,350)(212,349)
(213,348)(214,347)(215,346)(216,345)(217,344)(218,343)(219,342)(220,341)
(221,340)(222,326)(223,338)(224,337)(225,336)(226,335)(227,334)(228,333)
(229,332)(230,331)(231,330)(232,329)(233,328)(234,327)(235,313)(236,325)
(237,324)(238,323)(239,322)(240,321)(241,320)(242,319)(243,318)(244,317)
(245,316)(246,315)(247,314)(248,300)(249,312)(250,311)(251,310)(252,309)
(253,308)(254,307)(255,306)(256,305)(257,304)(258,303)(259,302)(260,301)
(261,287)(262,299)(263,298)(264,297)(265,296)(266,295)(267,294)(268,293)
(269,292)(270,291)(271,290)(272,289)(273,288);;
s1 := ( 1,197)( 2,196)( 3,208)( 4,207)( 5,206)( 6,205)( 7,204)( 8,203)
( 9,202)( 10,201)( 11,200)( 12,199)( 13,198)( 14,184)( 15,183)( 16,195)
( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,188)( 24,187)
( 25,186)( 26,185)( 27,262)( 28,261)( 29,273)( 30,272)( 31,271)( 32,270)
( 33,269)( 34,268)( 35,267)( 36,266)( 37,265)( 38,264)( 39,263)( 40,249)
( 41,248)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,255)( 48,254)
( 49,253)( 50,252)( 51,251)( 52,250)( 53,236)( 54,235)( 55,247)( 56,246)
( 57,245)( 58,244)( 59,243)( 60,242)( 61,241)( 62,240)( 63,239)( 64,238)
( 65,237)( 66,223)( 67,222)( 68,234)( 69,233)( 70,232)( 71,231)( 72,230)
( 73,229)( 74,228)( 75,227)( 76,226)( 77,225)( 78,224)( 79,210)( 80,209)
( 81,221)( 82,220)( 83,219)( 84,218)( 85,217)( 86,216)( 87,215)( 88,214)
( 89,213)( 90,212)( 91,211)( 92,288)( 93,287)( 94,299)( 95,298)( 96,297)
( 97,296)( 98,295)( 99,294)(100,293)(101,292)(102,291)(103,290)(104,289)
(105,275)(106,274)(107,286)(108,285)(109,284)(110,283)(111,282)(112,281)
(113,280)(114,279)(115,278)(116,277)(117,276)(118,353)(119,352)(120,364)
(121,363)(122,362)(123,361)(124,360)(125,359)(126,358)(127,357)(128,356)
(129,355)(130,354)(131,340)(132,339)(133,351)(134,350)(135,349)(136,348)
(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)(144,327)
(145,326)(146,338)(147,337)(148,336)(149,335)(150,334)(151,333)(152,332)
(153,331)(154,330)(155,329)(156,328)(157,314)(158,313)(159,325)(160,324)
(161,323)(162,322)(163,321)(164,320)(165,319)(166,318)(167,317)(168,316)
(169,315)(170,301)(171,300)(172,312)(173,311)(174,310)(175,309)(176,308)
(177,307)(178,306)(179,305)(180,304)(181,303)(182,302);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(364)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 14, 79)
( 15, 91)( 16, 90)( 17, 89)( 18, 88)( 19, 87)( 20, 86)( 21, 85)( 22, 84)
( 23, 83)( 24, 82)( 25, 81)( 26, 80)( 27, 66)( 28, 78)( 29, 77)( 30, 76)
( 31, 75)( 32, 74)( 33, 73)( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)
( 39, 67)( 40, 53)( 41, 65)( 42, 64)( 43, 63)( 44, 62)( 45, 61)( 46, 60)
( 47, 59)( 48, 58)( 49, 57)( 50, 56)( 51, 55)( 52, 54)( 93,104)( 94,103)
( 95,102)( 96,101)( 97,100)( 98, 99)(105,170)(106,182)(107,181)(108,180)
(109,179)(110,178)(111,177)(112,176)(113,175)(114,174)(115,173)(116,172)
(117,171)(118,157)(119,169)(120,168)(121,167)(122,166)(123,165)(124,164)
(125,163)(126,162)(127,161)(128,160)(129,159)(130,158)(131,144)(132,156)
(133,155)(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)
(141,147)(142,146)(143,145)(183,274)(184,286)(185,285)(186,284)(187,283)
(188,282)(189,281)(190,280)(191,279)(192,278)(193,277)(194,276)(195,275)
(196,352)(197,364)(198,363)(199,362)(200,361)(201,360)(202,359)(203,358)
(204,357)(205,356)(206,355)(207,354)(208,353)(209,339)(210,351)(211,350)
(212,349)(213,348)(214,347)(215,346)(216,345)(217,344)(218,343)(219,342)
(220,341)(221,340)(222,326)(223,338)(224,337)(225,336)(226,335)(227,334)
(228,333)(229,332)(230,331)(231,330)(232,329)(233,328)(234,327)(235,313)
(236,325)(237,324)(238,323)(239,322)(240,321)(241,320)(242,319)(243,318)
(244,317)(245,316)(246,315)(247,314)(248,300)(249,312)(250,311)(251,310)
(252,309)(253,308)(254,307)(255,306)(256,305)(257,304)(258,303)(259,302)
(260,301)(261,287)(262,299)(263,298)(264,297)(265,296)(266,295)(267,294)
(268,293)(269,292)(270,291)(271,290)(272,289)(273,288);
s1 := Sym(364)!( 1,197)( 2,196)( 3,208)( 4,207)( 5,206)( 6,205)( 7,204)
( 8,203)( 9,202)( 10,201)( 11,200)( 12,199)( 13,198)( 14,184)( 15,183)
( 16,195)( 17,194)( 18,193)( 19,192)( 20,191)( 21,190)( 22,189)( 23,188)
( 24,187)( 25,186)( 26,185)( 27,262)( 28,261)( 29,273)( 30,272)( 31,271)
( 32,270)( 33,269)( 34,268)( 35,267)( 36,266)( 37,265)( 38,264)( 39,263)
( 40,249)( 41,248)( 42,260)( 43,259)( 44,258)( 45,257)( 46,256)( 47,255)
( 48,254)( 49,253)( 50,252)( 51,251)( 52,250)( 53,236)( 54,235)( 55,247)
( 56,246)( 57,245)( 58,244)( 59,243)( 60,242)( 61,241)( 62,240)( 63,239)
( 64,238)( 65,237)( 66,223)( 67,222)( 68,234)( 69,233)( 70,232)( 71,231)
( 72,230)( 73,229)( 74,228)( 75,227)( 76,226)( 77,225)( 78,224)( 79,210)
( 80,209)( 81,221)( 82,220)( 83,219)( 84,218)( 85,217)( 86,216)( 87,215)
( 88,214)( 89,213)( 90,212)( 91,211)( 92,288)( 93,287)( 94,299)( 95,298)
( 96,297)( 97,296)( 98,295)( 99,294)(100,293)(101,292)(102,291)(103,290)
(104,289)(105,275)(106,274)(107,286)(108,285)(109,284)(110,283)(111,282)
(112,281)(113,280)(114,279)(115,278)(116,277)(117,276)(118,353)(119,352)
(120,364)(121,363)(122,362)(123,361)(124,360)(125,359)(126,358)(127,357)
(128,356)(129,355)(130,354)(131,340)(132,339)(133,351)(134,350)(135,349)
(136,348)(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)
(144,327)(145,326)(146,338)(147,337)(148,336)(149,335)(150,334)(151,333)
(152,332)(153,331)(154,330)(155,329)(156,328)(157,314)(158,313)(159,325)
(160,324)(161,323)(162,322)(163,321)(164,320)(165,319)(166,318)(167,317)
(168,316)(169,315)(170,301)(171,300)(172,312)(173,311)(174,310)(175,309)
(176,308)(177,307)(178,306)(179,305)(180,304)(181,303)(182,302);
poly := sub<Sym(364)|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 >;
References : None.
to this polytope