Polytope of Type {292}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {292}*584
Also Known As : 292-gon, {292}. if this polytope has another name.
Group : SmallGroup(584,6)
Rank : 2
Schlafli Type : {292}
Number of vertices, edges, etc : 292, 292
Order of s0s1 : 292
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{292,2} of size 1168
Vertex Figure Of :
{2,292} of size 1168
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {146}*292
4-fold quotients : {73}*146
73-fold quotients : {4}*8
146-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {584}*1168
3-fold covers : {876}*1752
Permutation Representation (GAP) :
s0 := ( 2, 73)( 3, 72)( 4, 71)( 5, 70)( 6, 69)( 7, 68)( 8, 67)( 9, 66)
( 10, 65)( 11, 64)( 12, 63)( 13, 62)( 14, 61)( 15, 60)( 16, 59)( 17, 58)
( 18, 57)( 19, 56)( 20, 55)( 21, 54)( 22, 53)( 23, 52)( 24, 51)( 25, 50)
( 26, 49)( 27, 48)( 28, 47)( 29, 46)( 30, 45)( 31, 44)( 32, 43)( 33, 42)
( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 75,146)( 76,145)( 77,144)( 78,143)
( 79,142)( 80,141)( 81,140)( 82,139)( 83,138)( 84,137)( 85,136)( 86,135)
( 87,134)( 88,133)( 89,132)( 90,131)( 91,130)( 92,129)( 93,128)( 94,127)
( 95,126)( 96,125)( 97,124)( 98,123)( 99,122)(100,121)(101,120)(102,119)
(103,118)(104,117)(105,116)(106,115)(107,114)(108,113)(109,112)(110,111)
(147,220)(148,292)(149,291)(150,290)(151,289)(152,288)(153,287)(154,286)
(155,285)(156,284)(157,283)(158,282)(159,281)(160,280)(161,279)(162,278)
(163,277)(164,276)(165,275)(166,274)(167,273)(168,272)(169,271)(170,270)
(171,269)(172,268)(173,267)(174,266)(175,265)(176,264)(177,263)(178,262)
(179,261)(180,260)(181,259)(182,258)(183,257)(184,256)(185,255)(186,254)
(187,253)(188,252)(189,251)(190,250)(191,249)(192,248)(193,247)(194,246)
(195,245)(196,244)(197,243)(198,242)(199,241)(200,240)(201,239)(202,238)
(203,237)(204,236)(205,235)(206,234)(207,233)(208,232)(209,231)(210,230)
(211,229)(212,228)(213,227)(214,226)(215,225)(216,224)(217,223)(218,222)
(219,221);;
s1 := ( 1,148)( 2,147)( 3,219)( 4,218)( 5,217)( 6,216)( 7,215)( 8,214)
( 9,213)( 10,212)( 11,211)( 12,210)( 13,209)( 14,208)( 15,207)( 16,206)
( 17,205)( 18,204)( 19,203)( 20,202)( 21,201)( 22,200)( 23,199)( 24,198)
( 25,197)( 26,196)( 27,195)( 28,194)( 29,193)( 30,192)( 31,191)( 32,190)
( 33,189)( 34,188)( 35,187)( 36,186)( 37,185)( 38,184)( 39,183)( 40,182)
( 41,181)( 42,180)( 43,179)( 44,178)( 45,177)( 46,176)( 47,175)( 48,174)
( 49,173)( 50,172)( 51,171)( 52,170)( 53,169)( 54,168)( 55,167)( 56,166)
( 57,165)( 58,164)( 59,163)( 60,162)( 61,161)( 62,160)( 63,159)( 64,158)
( 65,157)( 66,156)( 67,155)( 68,154)( 69,153)( 70,152)( 71,151)( 72,150)
( 73,149)( 74,221)( 75,220)( 76,292)( 77,291)( 78,290)( 79,289)( 80,288)
( 81,287)( 82,286)( 83,285)( 84,284)( 85,283)( 86,282)( 87,281)( 88,280)
( 89,279)( 90,278)( 91,277)( 92,276)( 93,275)( 94,274)( 95,273)( 96,272)
( 97,271)( 98,270)( 99,269)(100,268)(101,267)(102,266)(103,265)(104,264)
(105,263)(106,262)(107,261)(108,260)(109,259)(110,258)(111,257)(112,256)
(113,255)(114,254)(115,253)(116,252)(117,251)(118,250)(119,249)(120,248)
(121,247)(122,246)(123,245)(124,244)(125,243)(126,242)(127,241)(128,240)
(129,239)(130,238)(131,237)(132,236)(133,235)(134,234)(135,233)(136,232)
(137,231)(138,230)(139,229)(140,228)(141,227)(142,226)(143,225)(144,224)
(145,223)(146,222);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(292)!( 2, 73)( 3, 72)( 4, 71)( 5, 70)( 6, 69)( 7, 68)( 8, 67)
( 9, 66)( 10, 65)( 11, 64)( 12, 63)( 13, 62)( 14, 61)( 15, 60)( 16, 59)
( 17, 58)( 18, 57)( 19, 56)( 20, 55)( 21, 54)( 22, 53)( 23, 52)( 24, 51)
( 25, 50)( 26, 49)( 27, 48)( 28, 47)( 29, 46)( 30, 45)( 31, 44)( 32, 43)
( 33, 42)( 34, 41)( 35, 40)( 36, 39)( 37, 38)( 75,146)( 76,145)( 77,144)
( 78,143)( 79,142)( 80,141)( 81,140)( 82,139)( 83,138)( 84,137)( 85,136)
( 86,135)( 87,134)( 88,133)( 89,132)( 90,131)( 91,130)( 92,129)( 93,128)
( 94,127)( 95,126)( 96,125)( 97,124)( 98,123)( 99,122)(100,121)(101,120)
(102,119)(103,118)(104,117)(105,116)(106,115)(107,114)(108,113)(109,112)
(110,111)(147,220)(148,292)(149,291)(150,290)(151,289)(152,288)(153,287)
(154,286)(155,285)(156,284)(157,283)(158,282)(159,281)(160,280)(161,279)
(162,278)(163,277)(164,276)(165,275)(166,274)(167,273)(168,272)(169,271)
(170,270)(171,269)(172,268)(173,267)(174,266)(175,265)(176,264)(177,263)
(178,262)(179,261)(180,260)(181,259)(182,258)(183,257)(184,256)(185,255)
(186,254)(187,253)(188,252)(189,251)(190,250)(191,249)(192,248)(193,247)
(194,246)(195,245)(196,244)(197,243)(198,242)(199,241)(200,240)(201,239)
(202,238)(203,237)(204,236)(205,235)(206,234)(207,233)(208,232)(209,231)
(210,230)(211,229)(212,228)(213,227)(214,226)(215,225)(216,224)(217,223)
(218,222)(219,221);
s1 := Sym(292)!( 1,148)( 2,147)( 3,219)( 4,218)( 5,217)( 6,216)( 7,215)
( 8,214)( 9,213)( 10,212)( 11,211)( 12,210)( 13,209)( 14,208)( 15,207)
( 16,206)( 17,205)( 18,204)( 19,203)( 20,202)( 21,201)( 22,200)( 23,199)
( 24,198)( 25,197)( 26,196)( 27,195)( 28,194)( 29,193)( 30,192)( 31,191)
( 32,190)( 33,189)( 34,188)( 35,187)( 36,186)( 37,185)( 38,184)( 39,183)
( 40,182)( 41,181)( 42,180)( 43,179)( 44,178)( 45,177)( 46,176)( 47,175)
( 48,174)( 49,173)( 50,172)( 51,171)( 52,170)( 53,169)( 54,168)( 55,167)
( 56,166)( 57,165)( 58,164)( 59,163)( 60,162)( 61,161)( 62,160)( 63,159)
( 64,158)( 65,157)( 66,156)( 67,155)( 68,154)( 69,153)( 70,152)( 71,151)
( 72,150)( 73,149)( 74,221)( 75,220)( 76,292)( 77,291)( 78,290)( 79,289)
( 80,288)( 81,287)( 82,286)( 83,285)( 84,284)( 85,283)( 86,282)( 87,281)
( 88,280)( 89,279)( 90,278)( 91,277)( 92,276)( 93,275)( 94,274)( 95,273)
( 96,272)( 97,271)( 98,270)( 99,269)(100,268)(101,267)(102,266)(103,265)
(104,264)(105,263)(106,262)(107,261)(108,260)(109,259)(110,258)(111,257)
(112,256)(113,255)(114,254)(115,253)(116,252)(117,251)(118,250)(119,249)
(120,248)(121,247)(122,246)(123,245)(124,244)(125,243)(126,242)(127,241)
(128,240)(129,239)(130,238)(131,237)(132,236)(133,235)(134,234)(135,233)
(136,232)(137,231)(138,230)(139,229)(140,228)(141,227)(142,226)(143,225)
(144,224)(145,223)(146,222);
poly := sub<Sym(292)|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 >;
References : None.
to this polytope