Polytope of Type {10,86}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,86}*1720
Also Known As : {10,86|2}. if this polytope has another name.
Group : SmallGroup(1720,35)
Rank : 3
Schlafli Type : {10,86}
Number of vertices, edges, etc : 10, 430, 86
Order of s0s1s2 : 430
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
5-fold quotients : {2,86}*344
10-fold quotients : {2,43}*172
43-fold quotients : {10,2}*40
86-fold quotients : {5,2}*20
215-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 44,173)( 45,174)( 46,175)( 47,176)( 48,177)( 49,178)( 50,179)( 51,180)
( 52,181)( 53,182)( 54,183)( 55,184)( 56,185)( 57,186)( 58,187)( 59,188)
( 60,189)( 61,190)( 62,191)( 63,192)( 64,193)( 65,194)( 66,195)( 67,196)
( 68,197)( 69,198)( 70,199)( 71,200)( 72,201)( 73,202)( 74,203)( 75,204)
( 76,205)( 77,206)( 78,207)( 79,208)( 80,209)( 81,210)( 82,211)( 83,212)
( 84,213)( 85,214)( 86,215)( 87,130)( 88,131)( 89,132)( 90,133)( 91,134)
( 92,135)( 93,136)( 94,137)( 95,138)( 96,139)( 97,140)( 98,141)( 99,142)
(100,143)(101,144)(102,145)(103,146)(104,147)(105,148)(106,149)(107,150)
(108,151)(109,152)(110,153)(111,154)(112,155)(113,156)(114,157)(115,158)
(116,159)(117,160)(118,161)(119,162)(120,163)(121,164)(122,165)(123,166)
(124,167)(125,168)(126,169)(127,170)(128,171)(129,172)(259,388)(260,389)
(261,390)(262,391)(263,392)(264,393)(265,394)(266,395)(267,396)(268,397)
(269,398)(270,399)(271,400)(272,401)(273,402)(274,403)(275,404)(276,405)
(277,406)(278,407)(279,408)(280,409)(281,410)(282,411)(283,412)(284,413)
(285,414)(286,415)(287,416)(288,417)(289,418)(290,419)(291,420)(292,421)
(293,422)(294,423)(295,424)(296,425)(297,426)(298,427)(299,428)(300,429)
(301,430)(302,345)(303,346)(304,347)(305,348)(306,349)(307,350)(308,351)
(309,352)(310,353)(311,354)(312,355)(313,356)(314,357)(315,358)(316,359)
(317,360)(318,361)(319,362)(320,363)(321,364)(322,365)(323,366)(324,367)
(325,368)(326,369)(327,370)(328,371)(329,372)(330,373)(331,374)(332,375)
(333,376)(334,377)(335,378)(336,379)(337,380)(338,381)(339,382)(340,383)
(341,384)(342,385)(343,386)(344,387);;
s1 := ( 1, 44)( 2, 86)( 3, 85)( 4, 84)( 5, 83)( 6, 82)( 7, 81)( 8, 80)
( 9, 79)( 10, 78)( 11, 77)( 12, 76)( 13, 75)( 14, 74)( 15, 73)( 16, 72)
( 17, 71)( 18, 70)( 19, 69)( 20, 68)( 21, 67)( 22, 66)( 23, 65)( 24, 64)
( 25, 63)( 26, 62)( 27, 61)( 28, 60)( 29, 59)( 30, 58)( 31, 57)( 32, 56)
( 33, 55)( 34, 54)( 35, 53)( 36, 52)( 37, 51)( 38, 50)( 39, 49)( 40, 48)
( 41, 47)( 42, 46)( 43, 45)( 87,173)( 88,215)( 89,214)( 90,213)( 91,212)
( 92,211)( 93,210)( 94,209)( 95,208)( 96,207)( 97,206)( 98,205)( 99,204)
(100,203)(101,202)(102,201)(103,200)(104,199)(105,198)(106,197)(107,196)
(108,195)(109,194)(110,193)(111,192)(112,191)(113,190)(114,189)(115,188)
(116,187)(117,186)(118,185)(119,184)(120,183)(121,182)(122,181)(123,180)
(124,179)(125,178)(126,177)(127,176)(128,175)(129,174)(131,172)(132,171)
(133,170)(134,169)(135,168)(136,167)(137,166)(138,165)(139,164)(140,163)
(141,162)(142,161)(143,160)(144,159)(145,158)(146,157)(147,156)(148,155)
(149,154)(150,153)(151,152)(216,259)(217,301)(218,300)(219,299)(220,298)
(221,297)(222,296)(223,295)(224,294)(225,293)(226,292)(227,291)(228,290)
(229,289)(230,288)(231,287)(232,286)(233,285)(234,284)(235,283)(236,282)
(237,281)(238,280)(239,279)(240,278)(241,277)(242,276)(243,275)(244,274)
(245,273)(246,272)(247,271)(248,270)(249,269)(250,268)(251,267)(252,266)
(253,265)(254,264)(255,263)(256,262)(257,261)(258,260)(302,388)(303,430)
(304,429)(305,428)(306,427)(307,426)(308,425)(309,424)(310,423)(311,422)
(312,421)(313,420)(314,419)(315,418)(316,417)(317,416)(318,415)(319,414)
(320,413)(321,412)(322,411)(323,410)(324,409)(325,408)(326,407)(327,406)
(328,405)(329,404)(330,403)(331,402)(332,401)(333,400)(334,399)(335,398)
(336,397)(337,396)(338,395)(339,394)(340,393)(341,392)(342,391)(343,390)
(344,389)(346,387)(347,386)(348,385)(349,384)(350,383)(351,382)(352,381)
(353,380)(354,379)(355,378)(356,377)(357,376)(358,375)(359,374)(360,373)
(361,372)(362,371)(363,370)(364,369)(365,368)(366,367);;
s2 := ( 1,217)( 2,216)( 3,258)( 4,257)( 5,256)( 6,255)( 7,254)( 8,253)
( 9,252)( 10,251)( 11,250)( 12,249)( 13,248)( 14,247)( 15,246)( 16,245)
( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,239)( 23,238)( 24,237)
( 25,236)( 26,235)( 27,234)( 28,233)( 29,232)( 30,231)( 31,230)( 32,229)
( 33,228)( 34,227)( 35,226)( 36,225)( 37,224)( 38,223)( 39,222)( 40,221)
( 41,220)( 42,219)( 43,218)( 44,260)( 45,259)( 46,301)( 47,300)( 48,299)
( 49,298)( 50,297)( 51,296)( 52,295)( 53,294)( 54,293)( 55,292)( 56,291)
( 57,290)( 58,289)( 59,288)( 60,287)( 61,286)( 62,285)( 63,284)( 64,283)
( 65,282)( 66,281)( 67,280)( 68,279)( 69,278)( 70,277)( 71,276)( 72,275)
( 73,274)( 74,273)( 75,272)( 76,271)( 77,270)( 78,269)( 79,268)( 80,267)
( 81,266)( 82,265)( 83,264)( 84,263)( 85,262)( 86,261)( 87,303)( 88,302)
( 89,344)( 90,343)( 91,342)( 92,341)( 93,340)( 94,339)( 95,338)( 96,337)
( 97,336)( 98,335)( 99,334)(100,333)(101,332)(102,331)(103,330)(104,329)
(105,328)(106,327)(107,326)(108,325)(109,324)(110,323)(111,322)(112,321)
(113,320)(114,319)(115,318)(116,317)(117,316)(118,315)(119,314)(120,313)
(121,312)(122,311)(123,310)(124,309)(125,308)(126,307)(127,306)(128,305)
(129,304)(130,346)(131,345)(132,387)(133,386)(134,385)(135,384)(136,383)
(137,382)(138,381)(139,380)(140,379)(141,378)(142,377)(143,376)(144,375)
(145,374)(146,373)(147,372)(148,371)(149,370)(150,369)(151,368)(152,367)
(153,366)(154,365)(155,364)(156,363)(157,362)(158,361)(159,360)(160,359)
(161,358)(162,357)(163,356)(164,355)(165,354)(166,353)(167,352)(168,351)
(169,350)(170,349)(171,348)(172,347)(173,389)(174,388)(175,430)(176,429)
(177,428)(178,427)(179,426)(180,425)(181,424)(182,423)(183,422)(184,421)
(185,420)(186,419)(187,418)(188,417)(189,416)(190,415)(191,414)(192,413)
(193,412)(194,411)(195,410)(196,409)(197,408)(198,407)(199,406)(200,405)
(201,404)(202,403)(203,402)(204,401)(205,400)(206,399)(207,398)(208,397)
(209,396)(210,395)(211,394)(212,393)(213,392)(214,391)(215,390);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(430)!( 44,173)( 45,174)( 46,175)( 47,176)( 48,177)( 49,178)( 50,179)
( 51,180)( 52,181)( 53,182)( 54,183)( 55,184)( 56,185)( 57,186)( 58,187)
( 59,188)( 60,189)( 61,190)( 62,191)( 63,192)( 64,193)( 65,194)( 66,195)
( 67,196)( 68,197)( 69,198)( 70,199)( 71,200)( 72,201)( 73,202)( 74,203)
( 75,204)( 76,205)( 77,206)( 78,207)( 79,208)( 80,209)( 81,210)( 82,211)
( 83,212)( 84,213)( 85,214)( 86,215)( 87,130)( 88,131)( 89,132)( 90,133)
( 91,134)( 92,135)( 93,136)( 94,137)( 95,138)( 96,139)( 97,140)( 98,141)
( 99,142)(100,143)(101,144)(102,145)(103,146)(104,147)(105,148)(106,149)
(107,150)(108,151)(109,152)(110,153)(111,154)(112,155)(113,156)(114,157)
(115,158)(116,159)(117,160)(118,161)(119,162)(120,163)(121,164)(122,165)
(123,166)(124,167)(125,168)(126,169)(127,170)(128,171)(129,172)(259,388)
(260,389)(261,390)(262,391)(263,392)(264,393)(265,394)(266,395)(267,396)
(268,397)(269,398)(270,399)(271,400)(272,401)(273,402)(274,403)(275,404)
(276,405)(277,406)(278,407)(279,408)(280,409)(281,410)(282,411)(283,412)
(284,413)(285,414)(286,415)(287,416)(288,417)(289,418)(290,419)(291,420)
(292,421)(293,422)(294,423)(295,424)(296,425)(297,426)(298,427)(299,428)
(300,429)(301,430)(302,345)(303,346)(304,347)(305,348)(306,349)(307,350)
(308,351)(309,352)(310,353)(311,354)(312,355)(313,356)(314,357)(315,358)
(316,359)(317,360)(318,361)(319,362)(320,363)(321,364)(322,365)(323,366)
(324,367)(325,368)(326,369)(327,370)(328,371)(329,372)(330,373)(331,374)
(332,375)(333,376)(334,377)(335,378)(336,379)(337,380)(338,381)(339,382)
(340,383)(341,384)(342,385)(343,386)(344,387);
s1 := Sym(430)!( 1, 44)( 2, 86)( 3, 85)( 4, 84)( 5, 83)( 6, 82)( 7, 81)
( 8, 80)( 9, 79)( 10, 78)( 11, 77)( 12, 76)( 13, 75)( 14, 74)( 15, 73)
( 16, 72)( 17, 71)( 18, 70)( 19, 69)( 20, 68)( 21, 67)( 22, 66)( 23, 65)
( 24, 64)( 25, 63)( 26, 62)( 27, 61)( 28, 60)( 29, 59)( 30, 58)( 31, 57)
( 32, 56)( 33, 55)( 34, 54)( 35, 53)( 36, 52)( 37, 51)( 38, 50)( 39, 49)
( 40, 48)( 41, 47)( 42, 46)( 43, 45)( 87,173)( 88,215)( 89,214)( 90,213)
( 91,212)( 92,211)( 93,210)( 94,209)( 95,208)( 96,207)( 97,206)( 98,205)
( 99,204)(100,203)(101,202)(102,201)(103,200)(104,199)(105,198)(106,197)
(107,196)(108,195)(109,194)(110,193)(111,192)(112,191)(113,190)(114,189)
(115,188)(116,187)(117,186)(118,185)(119,184)(120,183)(121,182)(122,181)
(123,180)(124,179)(125,178)(126,177)(127,176)(128,175)(129,174)(131,172)
(132,171)(133,170)(134,169)(135,168)(136,167)(137,166)(138,165)(139,164)
(140,163)(141,162)(142,161)(143,160)(144,159)(145,158)(146,157)(147,156)
(148,155)(149,154)(150,153)(151,152)(216,259)(217,301)(218,300)(219,299)
(220,298)(221,297)(222,296)(223,295)(224,294)(225,293)(226,292)(227,291)
(228,290)(229,289)(230,288)(231,287)(232,286)(233,285)(234,284)(235,283)
(236,282)(237,281)(238,280)(239,279)(240,278)(241,277)(242,276)(243,275)
(244,274)(245,273)(246,272)(247,271)(248,270)(249,269)(250,268)(251,267)
(252,266)(253,265)(254,264)(255,263)(256,262)(257,261)(258,260)(302,388)
(303,430)(304,429)(305,428)(306,427)(307,426)(308,425)(309,424)(310,423)
(311,422)(312,421)(313,420)(314,419)(315,418)(316,417)(317,416)(318,415)
(319,414)(320,413)(321,412)(322,411)(323,410)(324,409)(325,408)(326,407)
(327,406)(328,405)(329,404)(330,403)(331,402)(332,401)(333,400)(334,399)
(335,398)(336,397)(337,396)(338,395)(339,394)(340,393)(341,392)(342,391)
(343,390)(344,389)(346,387)(347,386)(348,385)(349,384)(350,383)(351,382)
(352,381)(353,380)(354,379)(355,378)(356,377)(357,376)(358,375)(359,374)
(360,373)(361,372)(362,371)(363,370)(364,369)(365,368)(366,367);
s2 := Sym(430)!( 1,217)( 2,216)( 3,258)( 4,257)( 5,256)( 6,255)( 7,254)
( 8,253)( 9,252)( 10,251)( 11,250)( 12,249)( 13,248)( 14,247)( 15,246)
( 16,245)( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,239)( 23,238)
( 24,237)( 25,236)( 26,235)( 27,234)( 28,233)( 29,232)( 30,231)( 31,230)
( 32,229)( 33,228)( 34,227)( 35,226)( 36,225)( 37,224)( 38,223)( 39,222)
( 40,221)( 41,220)( 42,219)( 43,218)( 44,260)( 45,259)( 46,301)( 47,300)
( 48,299)( 49,298)( 50,297)( 51,296)( 52,295)( 53,294)( 54,293)( 55,292)
( 56,291)( 57,290)( 58,289)( 59,288)( 60,287)( 61,286)( 62,285)( 63,284)
( 64,283)( 65,282)( 66,281)( 67,280)( 68,279)( 69,278)( 70,277)( 71,276)
( 72,275)( 73,274)( 74,273)( 75,272)( 76,271)( 77,270)( 78,269)( 79,268)
( 80,267)( 81,266)( 82,265)( 83,264)( 84,263)( 85,262)( 86,261)( 87,303)
( 88,302)( 89,344)( 90,343)( 91,342)( 92,341)( 93,340)( 94,339)( 95,338)
( 96,337)( 97,336)( 98,335)( 99,334)(100,333)(101,332)(102,331)(103,330)
(104,329)(105,328)(106,327)(107,326)(108,325)(109,324)(110,323)(111,322)
(112,321)(113,320)(114,319)(115,318)(116,317)(117,316)(118,315)(119,314)
(120,313)(121,312)(122,311)(123,310)(124,309)(125,308)(126,307)(127,306)
(128,305)(129,304)(130,346)(131,345)(132,387)(133,386)(134,385)(135,384)
(136,383)(137,382)(138,381)(139,380)(140,379)(141,378)(142,377)(143,376)
(144,375)(145,374)(146,373)(147,372)(148,371)(149,370)(150,369)(151,368)
(152,367)(153,366)(154,365)(155,364)(156,363)(157,362)(158,361)(159,360)
(160,359)(161,358)(162,357)(163,356)(164,355)(165,354)(166,353)(167,352)
(168,351)(169,350)(170,349)(171,348)(172,347)(173,389)(174,388)(175,430)
(176,429)(177,428)(178,427)(179,426)(180,425)(181,424)(182,423)(183,422)
(184,421)(185,420)(186,419)(187,418)(188,417)(189,416)(190,415)(191,414)
(192,413)(193,412)(194,411)(195,410)(196,409)(197,408)(198,407)(199,406)
(200,405)(201,404)(202,403)(203,402)(204,401)(205,400)(206,399)(207,398)
(208,397)(209,396)(210,395)(211,394)(212,393)(213,392)(214,391)(215,390);
poly := sub<Sym(430)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope