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