Polytope of Type {88,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {88,10}*1760
Also Known As : {88,10|2}. if this polytope has another name.
Group : SmallGroup(1760,479)
Rank : 3
Schlafli Type : {88,10}
Number of vertices, edges, etc : 88, 440, 10
Order of s0s1s2 : 440
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) :
2-fold quotients : {44,10}*880
4-fold quotients : {22,10}*440
5-fold quotients : {88,2}*352
10-fold quotients : {44,2}*176
11-fold quotients : {8,10}*160
20-fold quotients : {22,2}*88
22-fold quotients : {4,10}*80
40-fold quotients : {11,2}*44
44-fold quotients : {2,10}*40
55-fold quotients : {8,2}*32
88-fold quotients : {2,5}*20
110-fold quotients : {4,2}*16
220-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)
( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)
( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)
( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)
( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)
(104,107)(105,106)(111,166)(112,176)(113,175)(114,174)(115,173)(116,172)
(117,171)(118,170)(119,169)(120,168)(121,167)(122,177)(123,187)(124,186)
(125,185)(126,184)(127,183)(128,182)(129,181)(130,180)(131,179)(132,178)
(133,188)(134,198)(135,197)(136,196)(137,195)(138,194)(139,193)(140,192)
(141,191)(142,190)(143,189)(144,199)(145,209)(146,208)(147,207)(148,206)
(149,205)(150,204)(151,203)(152,202)(153,201)(154,200)(155,210)(156,220)
(157,219)(158,218)(159,217)(160,216)(161,215)(162,214)(163,213)(164,212)
(165,211)(221,331)(222,341)(223,340)(224,339)(225,338)(226,337)(227,336)
(228,335)(229,334)(230,333)(231,332)(232,342)(233,352)(234,351)(235,350)
(236,349)(237,348)(238,347)(239,346)(240,345)(241,344)(242,343)(243,353)
(244,363)(245,362)(246,361)(247,360)(248,359)(249,358)(250,357)(251,356)
(252,355)(253,354)(254,364)(255,374)(256,373)(257,372)(258,371)(259,370)
(260,369)(261,368)(262,367)(263,366)(264,365)(265,375)(266,385)(267,384)
(268,383)(269,382)(270,381)(271,380)(272,379)(273,378)(274,377)(275,376)
(276,386)(277,396)(278,395)(279,394)(280,393)(281,392)(282,391)(283,390)
(284,389)(285,388)(286,387)(287,397)(288,407)(289,406)(290,405)(291,404)
(292,403)(293,402)(294,401)(295,400)(296,399)(297,398)(298,408)(299,418)
(300,417)(301,416)(302,415)(303,414)(304,413)(305,412)(306,411)(307,410)
(308,409)(309,419)(310,429)(311,428)(312,427)(313,426)(314,425)(315,424)
(316,423)(317,422)(318,421)(319,420)(320,430)(321,440)(322,439)(323,438)
(324,437)(325,436)(326,435)(327,434)(328,433)(329,432)(330,431);;
s1 := ( 1,222)( 2,221)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)( 8,226)
( 9,225)( 10,224)( 11,223)( 12,266)( 13,265)( 14,275)( 15,274)( 16,273)
( 17,272)( 18,271)( 19,270)( 20,269)( 21,268)( 22,267)( 23,255)( 24,254)
( 25,264)( 26,263)( 27,262)( 28,261)( 29,260)( 30,259)( 31,258)( 32,257)
( 33,256)( 34,244)( 35,243)( 36,253)( 37,252)( 38,251)( 39,250)( 40,249)
( 41,248)( 42,247)( 43,246)( 44,245)( 45,233)( 46,232)( 47,242)( 48,241)
( 49,240)( 50,239)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)( 56,277)
( 57,276)( 58,286)( 59,285)( 60,284)( 61,283)( 62,282)( 63,281)( 64,280)
( 65,279)( 66,278)( 67,321)( 68,320)( 69,330)( 70,329)( 71,328)( 72,327)
( 73,326)( 74,325)( 75,324)( 76,323)( 77,322)( 78,310)( 79,309)( 80,319)
( 81,318)( 82,317)( 83,316)( 84,315)( 85,314)( 86,313)( 87,312)( 88,311)
( 89,299)( 90,298)( 91,308)( 92,307)( 93,306)( 94,305)( 95,304)( 96,303)
( 97,302)( 98,301)( 99,300)(100,288)(101,287)(102,297)(103,296)(104,295)
(105,294)(106,293)(107,292)(108,291)(109,290)(110,289)(111,387)(112,386)
(113,396)(114,395)(115,394)(116,393)(117,392)(118,391)(119,390)(120,389)
(121,388)(122,431)(123,430)(124,440)(125,439)(126,438)(127,437)(128,436)
(129,435)(130,434)(131,433)(132,432)(133,420)(134,419)(135,429)(136,428)
(137,427)(138,426)(139,425)(140,424)(141,423)(142,422)(143,421)(144,409)
(145,408)(146,418)(147,417)(148,416)(149,415)(150,414)(151,413)(152,412)
(153,411)(154,410)(155,398)(156,397)(157,407)(158,406)(159,405)(160,404)
(161,403)(162,402)(163,401)(164,400)(165,399)(166,332)(167,331)(168,341)
(169,340)(170,339)(171,338)(172,337)(173,336)(174,335)(175,334)(176,333)
(177,376)(178,375)(179,385)(180,384)(181,383)(182,382)(183,381)(184,380)
(185,379)(186,378)(187,377)(188,365)(189,364)(190,374)(191,373)(192,372)
(193,371)(194,370)(195,369)(196,368)(197,367)(198,366)(199,354)(200,353)
(201,363)(202,362)(203,361)(204,360)(205,359)(206,358)(207,357)(208,356)
(209,355)(210,343)(211,342)(212,352)(213,351)(214,350)(215,349)(216,348)
(217,347)(218,346)(219,345)(220,344);;
s2 := ( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 16)( 6, 17)( 7, 18)( 8, 19)
( 9, 20)( 10, 21)( 11, 22)( 23, 45)( 24, 46)( 25, 47)( 26, 48)( 27, 49)
( 28, 50)( 29, 51)( 30, 52)( 31, 53)( 32, 54)( 33, 55)( 56, 67)( 57, 68)
( 58, 69)( 59, 70)( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)( 65, 76)
( 66, 77)( 78,100)( 79,101)( 80,102)( 81,103)( 82,104)( 83,105)( 84,106)
( 85,107)( 86,108)( 87,109)( 88,110)(111,122)(112,123)(113,124)(114,125)
(115,126)(116,127)(117,128)(118,129)(119,130)(120,131)(121,132)(133,155)
(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)(141,163)
(142,164)(143,165)(166,177)(167,178)(168,179)(169,180)(170,181)(171,182)
(172,183)(173,184)(174,185)(175,186)(176,187)(188,210)(189,211)(190,212)
(191,213)(192,214)(193,215)(194,216)(195,217)(196,218)(197,219)(198,220)
(221,232)(222,233)(223,234)(224,235)(225,236)(226,237)(227,238)(228,239)
(229,240)(230,241)(231,242)(243,265)(244,266)(245,267)(246,268)(247,269)
(248,270)(249,271)(250,272)(251,273)(252,274)(253,275)(276,287)(277,288)
(278,289)(279,290)(280,291)(281,292)(282,293)(283,294)(284,295)(285,296)
(286,297)(298,320)(299,321)(300,322)(301,323)(302,324)(303,325)(304,326)
(305,327)(306,328)(307,329)(308,330)(331,342)(332,343)(333,344)(334,345)
(335,346)(336,347)(337,348)(338,349)(339,350)(340,351)(341,352)(353,375)
(354,376)(355,377)(356,378)(357,379)(358,380)(359,381)(360,382)(361,383)
(362,384)(363,385)(386,397)(387,398)(388,399)(389,400)(390,401)(391,402)
(392,403)(393,404)(394,405)(395,406)(396,407)(408,430)(409,431)(410,432)
(411,433)(412,434)(413,435)(414,436)(415,437)(416,438)(417,439)(418,440);;
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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(440)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)
( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)
( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)
(103,108)(104,107)(105,106)(111,166)(112,176)(113,175)(114,174)(115,173)
(116,172)(117,171)(118,170)(119,169)(120,168)(121,167)(122,177)(123,187)
(124,186)(125,185)(126,184)(127,183)(128,182)(129,181)(130,180)(131,179)
(132,178)(133,188)(134,198)(135,197)(136,196)(137,195)(138,194)(139,193)
(140,192)(141,191)(142,190)(143,189)(144,199)(145,209)(146,208)(147,207)
(148,206)(149,205)(150,204)(151,203)(152,202)(153,201)(154,200)(155,210)
(156,220)(157,219)(158,218)(159,217)(160,216)(161,215)(162,214)(163,213)
(164,212)(165,211)(221,331)(222,341)(223,340)(224,339)(225,338)(226,337)
(227,336)(228,335)(229,334)(230,333)(231,332)(232,342)(233,352)(234,351)
(235,350)(236,349)(237,348)(238,347)(239,346)(240,345)(241,344)(242,343)
(243,353)(244,363)(245,362)(246,361)(247,360)(248,359)(249,358)(250,357)
(251,356)(252,355)(253,354)(254,364)(255,374)(256,373)(257,372)(258,371)
(259,370)(260,369)(261,368)(262,367)(263,366)(264,365)(265,375)(266,385)
(267,384)(268,383)(269,382)(270,381)(271,380)(272,379)(273,378)(274,377)
(275,376)(276,386)(277,396)(278,395)(279,394)(280,393)(281,392)(282,391)
(283,390)(284,389)(285,388)(286,387)(287,397)(288,407)(289,406)(290,405)
(291,404)(292,403)(293,402)(294,401)(295,400)(296,399)(297,398)(298,408)
(299,418)(300,417)(301,416)(302,415)(303,414)(304,413)(305,412)(306,411)
(307,410)(308,409)(309,419)(310,429)(311,428)(312,427)(313,426)(314,425)
(315,424)(316,423)(317,422)(318,421)(319,420)(320,430)(321,440)(322,439)
(323,438)(324,437)(325,436)(326,435)(327,434)(328,433)(329,432)(330,431);
s1 := Sym(440)!( 1,222)( 2,221)( 3,231)( 4,230)( 5,229)( 6,228)( 7,227)
( 8,226)( 9,225)( 10,224)( 11,223)( 12,266)( 13,265)( 14,275)( 15,274)
( 16,273)( 17,272)( 18,271)( 19,270)( 20,269)( 21,268)( 22,267)( 23,255)
( 24,254)( 25,264)( 26,263)( 27,262)( 28,261)( 29,260)( 30,259)( 31,258)
( 32,257)( 33,256)( 34,244)( 35,243)( 36,253)( 37,252)( 38,251)( 39,250)
( 40,249)( 41,248)( 42,247)( 43,246)( 44,245)( 45,233)( 46,232)( 47,242)
( 48,241)( 49,240)( 50,239)( 51,238)( 52,237)( 53,236)( 54,235)( 55,234)
( 56,277)( 57,276)( 58,286)( 59,285)( 60,284)( 61,283)( 62,282)( 63,281)
( 64,280)( 65,279)( 66,278)( 67,321)( 68,320)( 69,330)( 70,329)( 71,328)
( 72,327)( 73,326)( 74,325)( 75,324)( 76,323)( 77,322)( 78,310)( 79,309)
( 80,319)( 81,318)( 82,317)( 83,316)( 84,315)( 85,314)( 86,313)( 87,312)
( 88,311)( 89,299)( 90,298)( 91,308)( 92,307)( 93,306)( 94,305)( 95,304)
( 96,303)( 97,302)( 98,301)( 99,300)(100,288)(101,287)(102,297)(103,296)
(104,295)(105,294)(106,293)(107,292)(108,291)(109,290)(110,289)(111,387)
(112,386)(113,396)(114,395)(115,394)(116,393)(117,392)(118,391)(119,390)
(120,389)(121,388)(122,431)(123,430)(124,440)(125,439)(126,438)(127,437)
(128,436)(129,435)(130,434)(131,433)(132,432)(133,420)(134,419)(135,429)
(136,428)(137,427)(138,426)(139,425)(140,424)(141,423)(142,422)(143,421)
(144,409)(145,408)(146,418)(147,417)(148,416)(149,415)(150,414)(151,413)
(152,412)(153,411)(154,410)(155,398)(156,397)(157,407)(158,406)(159,405)
(160,404)(161,403)(162,402)(163,401)(164,400)(165,399)(166,332)(167,331)
(168,341)(169,340)(170,339)(171,338)(172,337)(173,336)(174,335)(175,334)
(176,333)(177,376)(178,375)(179,385)(180,384)(181,383)(182,382)(183,381)
(184,380)(185,379)(186,378)(187,377)(188,365)(189,364)(190,374)(191,373)
(192,372)(193,371)(194,370)(195,369)(196,368)(197,367)(198,366)(199,354)
(200,353)(201,363)(202,362)(203,361)(204,360)(205,359)(206,358)(207,357)
(208,356)(209,355)(210,343)(211,342)(212,352)(213,351)(214,350)(215,349)
(216,348)(217,347)(218,346)(219,345)(220,344);
s2 := Sym(440)!( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 16)( 6, 17)( 7, 18)
( 8, 19)( 9, 20)( 10, 21)( 11, 22)( 23, 45)( 24, 46)( 25, 47)( 26, 48)
( 27, 49)( 28, 50)( 29, 51)( 30, 52)( 31, 53)( 32, 54)( 33, 55)( 56, 67)
( 57, 68)( 58, 69)( 59, 70)( 60, 71)( 61, 72)( 62, 73)( 63, 74)( 64, 75)
( 65, 76)( 66, 77)( 78,100)( 79,101)( 80,102)( 81,103)( 82,104)( 83,105)
( 84,106)( 85,107)( 86,108)( 87,109)( 88,110)(111,122)(112,123)(113,124)
(114,125)(115,126)(116,127)(117,128)(118,129)(119,130)(120,131)(121,132)
(133,155)(134,156)(135,157)(136,158)(137,159)(138,160)(139,161)(140,162)
(141,163)(142,164)(143,165)(166,177)(167,178)(168,179)(169,180)(170,181)
(171,182)(172,183)(173,184)(174,185)(175,186)(176,187)(188,210)(189,211)
(190,212)(191,213)(192,214)(193,215)(194,216)(195,217)(196,218)(197,219)
(198,220)(221,232)(222,233)(223,234)(224,235)(225,236)(226,237)(227,238)
(228,239)(229,240)(230,241)(231,242)(243,265)(244,266)(245,267)(246,268)
(247,269)(248,270)(249,271)(250,272)(251,273)(252,274)(253,275)(276,287)
(277,288)(278,289)(279,290)(280,291)(281,292)(282,293)(283,294)(284,295)
(285,296)(286,297)(298,320)(299,321)(300,322)(301,323)(302,324)(303,325)
(304,326)(305,327)(306,328)(307,329)(308,330)(331,342)(332,343)(333,344)
(334,345)(335,346)(336,347)(337,348)(338,349)(339,350)(340,351)(341,352)
(353,375)(354,376)(355,377)(356,378)(357,379)(358,380)(359,381)(360,382)
(361,383)(362,384)(363,385)(386,397)(387,398)(388,399)(389,400)(390,401)
(391,402)(392,403)(393,404)(394,405)(395,406)(396,407)(408,430)(409,431)
(410,432)(411,433)(412,434)(413,435)(414,436)(415,437)(416,438)(417,439)
(418,440);
poly := sub<Sym(440)|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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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