Polytope of Type {110,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {110,8}*1760
Also Known As : {110,8|2}. if this polytope has another name.
Group : SmallGroup(1760,1018)
Rank : 3
Schlafli Type : {110,8}
Number of vertices, edges, etc : 110, 440, 8
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 : {110,4}*880
4-fold quotients : {110,2}*440
5-fold quotients : {22,8}*352
8-fold quotients : {55,2}*220
10-fold quotients : {22,4}*176
11-fold quotients : {10,8}*160
20-fold quotients : {22,2}*88
22-fold quotients : {10,4}*80
40-fold quotients : {11,2}*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 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 12, 45)( 13, 55)( 14, 54)
( 15, 53)( 16, 52)( 17, 51)( 18, 50)( 19, 49)( 20, 48)( 21, 47)( 22, 46)
( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)( 29, 39)( 30, 38)
( 31, 37)( 32, 36)( 33, 35)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)
( 67,100)( 68,110)( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)( 74,104)
( 75,103)( 76,102)( 77,101)( 78, 89)( 79, 99)( 80, 98)( 81, 97)( 82, 96)
( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)( 88, 90)(112,121)(113,120)
(114,119)(115,118)(116,117)(122,155)(123,165)(124,164)(125,163)(126,162)
(127,161)(128,160)(129,159)(130,158)(131,157)(132,156)(133,144)(134,154)
(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)(142,146)
(143,145)(167,176)(168,175)(169,174)(170,173)(171,172)(177,210)(178,220)
(179,219)(180,218)(181,217)(182,216)(183,215)(184,214)(185,213)(186,212)
(187,211)(188,199)(189,209)(190,208)(191,207)(192,206)(193,205)(194,204)
(195,203)(196,202)(197,201)(198,200)(222,231)(223,230)(224,229)(225,228)
(226,227)(232,265)(233,275)(234,274)(235,273)(236,272)(237,271)(238,270)
(239,269)(240,268)(241,267)(242,266)(243,254)(244,264)(245,263)(246,262)
(247,261)(248,260)(249,259)(250,258)(251,257)(252,256)(253,255)(277,286)
(278,285)(279,284)(280,283)(281,282)(287,320)(288,330)(289,329)(290,328)
(291,327)(292,326)(293,325)(294,324)(295,323)(296,322)(297,321)(298,309)
(299,319)(300,318)(301,317)(302,316)(303,315)(304,314)(305,313)(306,312)
(307,311)(308,310)(332,341)(333,340)(334,339)(335,338)(336,337)(342,375)
(343,385)(344,384)(345,383)(346,382)(347,381)(348,380)(349,379)(350,378)
(351,377)(352,376)(353,364)(354,374)(355,373)(356,372)(357,371)(358,370)
(359,369)(360,368)(361,367)(362,366)(363,365)(387,396)(388,395)(389,394)
(390,393)(391,392)(397,430)(398,440)(399,439)(400,438)(401,437)(402,436)
(403,435)(404,434)(405,433)(406,432)(407,431)(408,419)(409,429)(410,428)
(411,427)(412,426)(413,425)(414,424)(415,423)(416,422)(417,421)(418,420);;
s1 := ( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)
( 9, 16)( 10, 15)( 11, 14)( 23, 46)( 24, 45)( 25, 55)( 26, 54)( 27, 53)
( 28, 52)( 29, 51)( 30, 50)( 31, 49)( 32, 48)( 33, 47)( 34, 35)( 36, 44)
( 37, 43)( 38, 42)( 39, 41)( 56, 68)( 57, 67)( 58, 77)( 59, 76)( 60, 75)
( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 78,101)( 79,100)
( 80,110)( 81,109)( 82,108)( 83,107)( 84,106)( 85,105)( 86,104)( 87,103)
( 88,102)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(111,178)(112,177)
(113,187)(114,186)(115,185)(116,184)(117,183)(118,182)(119,181)(120,180)
(121,179)(122,167)(123,166)(124,176)(125,175)(126,174)(127,173)(128,172)
(129,171)(130,170)(131,169)(132,168)(133,211)(134,210)(135,220)(136,219)
(137,218)(138,217)(139,216)(140,215)(141,214)(142,213)(143,212)(144,200)
(145,199)(146,209)(147,208)(148,207)(149,206)(150,205)(151,204)(152,203)
(153,202)(154,201)(155,189)(156,188)(157,198)(158,197)(159,196)(160,195)
(161,194)(162,193)(163,192)(164,191)(165,190)(221,343)(222,342)(223,352)
(224,351)(225,350)(226,349)(227,348)(228,347)(229,346)(230,345)(231,344)
(232,332)(233,331)(234,341)(235,340)(236,339)(237,338)(238,337)(239,336)
(240,335)(241,334)(242,333)(243,376)(244,375)(245,385)(246,384)(247,383)
(248,382)(249,381)(250,380)(251,379)(252,378)(253,377)(254,365)(255,364)
(256,374)(257,373)(258,372)(259,371)(260,370)(261,369)(262,368)(263,367)
(264,366)(265,354)(266,353)(267,363)(268,362)(269,361)(270,360)(271,359)
(272,358)(273,357)(274,356)(275,355)(276,398)(277,397)(278,407)(279,406)
(280,405)(281,404)(282,403)(283,402)(284,401)(285,400)(286,399)(287,387)
(288,386)(289,396)(290,395)(291,394)(292,393)(293,392)(294,391)(295,390)
(296,389)(297,388)(298,431)(299,430)(300,440)(301,439)(302,438)(303,437)
(304,436)(305,435)(306,434)(307,433)(308,432)(309,420)(310,419)(311,429)
(312,428)(313,427)(314,426)(315,425)(316,424)(317,423)(318,422)(319,421)
(320,409)(321,408)(322,418)(323,417)(324,416)(325,415)(326,414)(327,413)
(328,412)(329,411)(330,410);;
s2 := ( 1,221)( 2,222)( 3,223)( 4,224)( 5,225)( 6,226)( 7,227)( 8,228)
( 9,229)( 10,230)( 11,231)( 12,232)( 13,233)( 14,234)( 15,235)( 16,236)
( 17,237)( 18,238)( 19,239)( 20,240)( 21,241)( 22,242)( 23,243)( 24,244)
( 25,245)( 26,246)( 27,247)( 28,248)( 29,249)( 30,250)( 31,251)( 32,252)
( 33,253)( 34,254)( 35,255)( 36,256)( 37,257)( 38,258)( 39,259)( 40,260)
( 41,261)( 42,262)( 43,263)( 44,264)( 45,265)( 46,266)( 47,267)( 48,268)
( 49,269)( 50,270)( 51,271)( 52,272)( 53,273)( 54,274)( 55,275)( 56,276)
( 57,277)( 58,278)( 59,279)( 60,280)( 61,281)( 62,282)( 63,283)( 64,284)
( 65,285)( 66,286)( 67,287)( 68,288)( 69,289)( 70,290)( 71,291)( 72,292)
( 73,293)( 74,294)( 75,295)( 76,296)( 77,297)( 78,298)( 79,299)( 80,300)
( 81,301)( 82,302)( 83,303)( 84,304)( 85,305)( 86,306)( 87,307)( 88,308)
( 89,309)( 90,310)( 91,311)( 92,312)( 93,313)( 94,314)( 95,315)( 96,316)
( 97,317)( 98,318)( 99,319)(100,320)(101,321)(102,322)(103,323)(104,324)
(105,325)(106,326)(107,327)(108,328)(109,329)(110,330)(111,386)(112,387)
(113,388)(114,389)(115,390)(116,391)(117,392)(118,393)(119,394)(120,395)
(121,396)(122,397)(123,398)(124,399)(125,400)(126,401)(127,402)(128,403)
(129,404)(130,405)(131,406)(132,407)(133,408)(134,409)(135,410)(136,411)
(137,412)(138,413)(139,414)(140,415)(141,416)(142,417)(143,418)(144,419)
(145,420)(146,421)(147,422)(148,423)(149,424)(150,425)(151,426)(152,427)
(153,428)(154,429)(155,430)(156,431)(157,432)(158,433)(159,434)(160,435)
(161,436)(162,437)(163,438)(164,439)(165,440)(166,331)(167,332)(168,333)
(169,334)(170,335)(171,336)(172,337)(173,338)(174,339)(175,340)(176,341)
(177,342)(178,343)(179,344)(180,345)(181,346)(182,347)(183,348)(184,349)
(185,350)(186,351)(187,352)(188,353)(189,354)(190,355)(191,356)(192,357)
(193,358)(194,359)(195,360)(196,361)(197,362)(198,363)(199,364)(200,365)
(201,366)(202,367)(203,368)(204,369)(205,370)(206,371)(207,372)(208,373)
(209,374)(210,375)(211,376)(212,377)(213,378)(214,379)(215,380)(216,381)
(217,382)(218,383)(219,384)(220,385);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 12, 45)( 13, 55)
( 14, 54)( 15, 53)( 16, 52)( 17, 51)( 18, 50)( 19, 49)( 20, 48)( 21, 47)
( 22, 46)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)( 29, 39)
( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 57, 66)( 58, 65)( 59, 64)( 60, 63)
( 61, 62)( 67,100)( 68,110)( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)
( 74,104)( 75,103)( 76,102)( 77,101)( 78, 89)( 79, 99)( 80, 98)( 81, 97)
( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)( 88, 90)(112,121)
(113,120)(114,119)(115,118)(116,117)(122,155)(123,165)(124,164)(125,163)
(126,162)(127,161)(128,160)(129,159)(130,158)(131,157)(132,156)(133,144)
(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)
(142,146)(143,145)(167,176)(168,175)(169,174)(170,173)(171,172)(177,210)
(178,220)(179,219)(180,218)(181,217)(182,216)(183,215)(184,214)(185,213)
(186,212)(187,211)(188,199)(189,209)(190,208)(191,207)(192,206)(193,205)
(194,204)(195,203)(196,202)(197,201)(198,200)(222,231)(223,230)(224,229)
(225,228)(226,227)(232,265)(233,275)(234,274)(235,273)(236,272)(237,271)
(238,270)(239,269)(240,268)(241,267)(242,266)(243,254)(244,264)(245,263)
(246,262)(247,261)(248,260)(249,259)(250,258)(251,257)(252,256)(253,255)
(277,286)(278,285)(279,284)(280,283)(281,282)(287,320)(288,330)(289,329)
(290,328)(291,327)(292,326)(293,325)(294,324)(295,323)(296,322)(297,321)
(298,309)(299,319)(300,318)(301,317)(302,316)(303,315)(304,314)(305,313)
(306,312)(307,311)(308,310)(332,341)(333,340)(334,339)(335,338)(336,337)
(342,375)(343,385)(344,384)(345,383)(346,382)(347,381)(348,380)(349,379)
(350,378)(351,377)(352,376)(353,364)(354,374)(355,373)(356,372)(357,371)
(358,370)(359,369)(360,368)(361,367)(362,366)(363,365)(387,396)(388,395)
(389,394)(390,393)(391,392)(397,430)(398,440)(399,439)(400,438)(401,437)
(402,436)(403,435)(404,434)(405,433)(406,432)(407,431)(408,419)(409,429)
(410,428)(411,427)(412,426)(413,425)(414,424)(415,423)(416,422)(417,421)
(418,420);
s1 := Sym(440)!( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)
( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 23, 46)( 24, 45)( 25, 55)( 26, 54)
( 27, 53)( 28, 52)( 29, 51)( 30, 50)( 31, 49)( 32, 48)( 33, 47)( 34, 35)
( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 56, 68)( 57, 67)( 58, 77)( 59, 76)
( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 78,101)
( 79,100)( 80,110)( 81,109)( 82,108)( 83,107)( 84,106)( 85,105)( 86,104)
( 87,103)( 88,102)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(111,178)
(112,177)(113,187)(114,186)(115,185)(116,184)(117,183)(118,182)(119,181)
(120,180)(121,179)(122,167)(123,166)(124,176)(125,175)(126,174)(127,173)
(128,172)(129,171)(130,170)(131,169)(132,168)(133,211)(134,210)(135,220)
(136,219)(137,218)(138,217)(139,216)(140,215)(141,214)(142,213)(143,212)
(144,200)(145,199)(146,209)(147,208)(148,207)(149,206)(150,205)(151,204)
(152,203)(153,202)(154,201)(155,189)(156,188)(157,198)(158,197)(159,196)
(160,195)(161,194)(162,193)(163,192)(164,191)(165,190)(221,343)(222,342)
(223,352)(224,351)(225,350)(226,349)(227,348)(228,347)(229,346)(230,345)
(231,344)(232,332)(233,331)(234,341)(235,340)(236,339)(237,338)(238,337)
(239,336)(240,335)(241,334)(242,333)(243,376)(244,375)(245,385)(246,384)
(247,383)(248,382)(249,381)(250,380)(251,379)(252,378)(253,377)(254,365)
(255,364)(256,374)(257,373)(258,372)(259,371)(260,370)(261,369)(262,368)
(263,367)(264,366)(265,354)(266,353)(267,363)(268,362)(269,361)(270,360)
(271,359)(272,358)(273,357)(274,356)(275,355)(276,398)(277,397)(278,407)
(279,406)(280,405)(281,404)(282,403)(283,402)(284,401)(285,400)(286,399)
(287,387)(288,386)(289,396)(290,395)(291,394)(292,393)(293,392)(294,391)
(295,390)(296,389)(297,388)(298,431)(299,430)(300,440)(301,439)(302,438)
(303,437)(304,436)(305,435)(306,434)(307,433)(308,432)(309,420)(310,419)
(311,429)(312,428)(313,427)(314,426)(315,425)(316,424)(317,423)(318,422)
(319,421)(320,409)(321,408)(322,418)(323,417)(324,416)(325,415)(326,414)
(327,413)(328,412)(329,411)(330,410);
s2 := Sym(440)!( 1,221)( 2,222)( 3,223)( 4,224)( 5,225)( 6,226)( 7,227)
( 8,228)( 9,229)( 10,230)( 11,231)( 12,232)( 13,233)( 14,234)( 15,235)
( 16,236)( 17,237)( 18,238)( 19,239)( 20,240)( 21,241)( 22,242)( 23,243)
( 24,244)( 25,245)( 26,246)( 27,247)( 28,248)( 29,249)( 30,250)( 31,251)
( 32,252)( 33,253)( 34,254)( 35,255)( 36,256)( 37,257)( 38,258)( 39,259)
( 40,260)( 41,261)( 42,262)( 43,263)( 44,264)( 45,265)( 46,266)( 47,267)
( 48,268)( 49,269)( 50,270)( 51,271)( 52,272)( 53,273)( 54,274)( 55,275)
( 56,276)( 57,277)( 58,278)( 59,279)( 60,280)( 61,281)( 62,282)( 63,283)
( 64,284)( 65,285)( 66,286)( 67,287)( 68,288)( 69,289)( 70,290)( 71,291)
( 72,292)( 73,293)( 74,294)( 75,295)( 76,296)( 77,297)( 78,298)( 79,299)
( 80,300)( 81,301)( 82,302)( 83,303)( 84,304)( 85,305)( 86,306)( 87,307)
( 88,308)( 89,309)( 90,310)( 91,311)( 92,312)( 93,313)( 94,314)( 95,315)
( 96,316)( 97,317)( 98,318)( 99,319)(100,320)(101,321)(102,322)(103,323)
(104,324)(105,325)(106,326)(107,327)(108,328)(109,329)(110,330)(111,386)
(112,387)(113,388)(114,389)(115,390)(116,391)(117,392)(118,393)(119,394)
(120,395)(121,396)(122,397)(123,398)(124,399)(125,400)(126,401)(127,402)
(128,403)(129,404)(130,405)(131,406)(132,407)(133,408)(134,409)(135,410)
(136,411)(137,412)(138,413)(139,414)(140,415)(141,416)(142,417)(143,418)
(144,419)(145,420)(146,421)(147,422)(148,423)(149,424)(150,425)(151,426)
(152,427)(153,428)(154,429)(155,430)(156,431)(157,432)(158,433)(159,434)
(160,435)(161,436)(162,437)(163,438)(164,439)(165,440)(166,331)(167,332)
(168,333)(169,334)(170,335)(171,336)(172,337)(173,338)(174,339)(175,340)
(176,341)(177,342)(178,343)(179,344)(180,345)(181,346)(182,347)(183,348)
(184,349)(185,350)(186,351)(187,352)(188,353)(189,354)(190,355)(191,356)
(192,357)(193,358)(194,359)(195,360)(196,361)(197,362)(198,363)(199,364)
(200,365)(201,366)(202,367)(203,368)(204,369)(205,370)(206,371)(207,372)
(208,373)(209,374)(210,375)(211,376)(212,377)(213,378)(214,379)(215,380)
(216,381)(217,382)(218,383)(219,384)(220,385);
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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