Polytope of Type {110,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {110,6}*1320
Also Known As : {110,6|2}. if this polytope has another name.
Group : SmallGroup(1320,171)
Rank : 3
Schlafli Type : {110,6}
Number of vertices, edges, etc : 110, 330, 6
Order of s0s1s2 : 330
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) :
3-fold quotients : {110,2}*440
5-fold quotients : {22,6}*264
6-fold quotients : {55,2}*220
11-fold quotients : {10,6}*120
15-fold quotients : {22,2}*88
30-fold quotients : {11,2}*44
33-fold quotients : {10,2}*40
55-fold quotients : {2,6}*24
66-fold quotients : {5,2}*20
110-fold quotients : {2,3}*12
165-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);;
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)( 56,123)( 57,122)( 58,132)( 59,131)( 60,130)
( 61,129)( 62,128)( 63,127)( 64,126)( 65,125)( 66,124)( 67,112)( 68,111)
( 69,121)( 70,120)( 71,119)( 72,118)( 73,117)( 74,116)( 75,115)( 76,114)
( 77,113)( 78,156)( 79,155)( 80,165)( 81,164)( 82,163)( 83,162)( 84,161)
( 85,160)( 86,159)( 87,158)( 88,157)( 89,145)( 90,144)( 91,154)( 92,153)
( 93,152)( 94,151)( 95,150)( 96,149)( 97,148)( 98,147)( 99,146)(100,134)
(101,133)(102,143)(103,142)(104,141)(105,140)(106,139)(107,138)(108,137)
(109,136)(110,135)(166,178)(167,177)(168,187)(169,186)(170,185)(171,184)
(172,183)(173,182)(174,181)(175,180)(176,179)(188,211)(189,210)(190,220)
(191,219)(192,218)(193,217)(194,216)(195,215)(196,214)(197,213)(198,212)
(199,200)(201,209)(202,208)(203,207)(204,206)(221,288)(222,287)(223,297)
(224,296)(225,295)(226,294)(227,293)(228,292)(229,291)(230,290)(231,289)
(232,277)(233,276)(234,286)(235,285)(236,284)(237,283)(238,282)(239,281)
(240,280)(241,279)(242,278)(243,321)(244,320)(245,330)(246,329)(247,328)
(248,327)(249,326)(250,325)(251,324)(252,323)(253,322)(254,310)(255,309)
(256,319)(257,318)(258,317)(259,316)(260,315)(261,314)(262,313)(263,312)
(264,311)(265,299)(266,298)(267,308)(268,307)(269,306)(270,305)(271,304)
(272,303)(273,302)(274,301)(275,300);;
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)( 56,166)
( 57,167)( 58,168)( 59,169)( 60,170)( 61,171)( 62,172)( 63,173)( 64,174)
( 65,175)( 66,176)( 67,177)( 68,178)( 69,179)( 70,180)( 71,181)( 72,182)
( 73,183)( 74,184)( 75,185)( 76,186)( 77,187)( 78,188)( 79,189)( 80,190)
( 81,191)( 82,192)( 83,193)( 84,194)( 85,195)( 86,196)( 87,197)( 88,198)
( 89,199)( 90,200)( 91,201)( 92,202)( 93,203)( 94,204)( 95,205)( 96,206)
( 97,207)( 98,208)( 99,209)(100,210)(101,211)(102,212)(103,213)(104,214)
(105,215)(106,216)(107,217)(108,218)(109,219)(110,220)(111,276)(112,277)
(113,278)(114,279)(115,280)(116,281)(117,282)(118,283)(119,284)(120,285)
(121,286)(122,287)(123,288)(124,289)(125,290)(126,291)(127,292)(128,293)
(129,294)(130,295)(131,296)(132,297)(133,298)(134,299)(135,300)(136,301)
(137,302)(138,303)(139,304)(140,305)(141,306)(142,307)(143,308)(144,309)
(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)(152,317)
(153,318)(154,319)(155,320)(156,321)(157,322)(158,323)(159,324)(160,325)
(161,326)(162,327)(163,328)(164,329)(165,330);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(330)!( 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);
s1 := Sym(330)!( 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)( 56,123)( 57,122)( 58,132)( 59,131)
( 60,130)( 61,129)( 62,128)( 63,127)( 64,126)( 65,125)( 66,124)( 67,112)
( 68,111)( 69,121)( 70,120)( 71,119)( 72,118)( 73,117)( 74,116)( 75,115)
( 76,114)( 77,113)( 78,156)( 79,155)( 80,165)( 81,164)( 82,163)( 83,162)
( 84,161)( 85,160)( 86,159)( 87,158)( 88,157)( 89,145)( 90,144)( 91,154)
( 92,153)( 93,152)( 94,151)( 95,150)( 96,149)( 97,148)( 98,147)( 99,146)
(100,134)(101,133)(102,143)(103,142)(104,141)(105,140)(106,139)(107,138)
(108,137)(109,136)(110,135)(166,178)(167,177)(168,187)(169,186)(170,185)
(171,184)(172,183)(173,182)(174,181)(175,180)(176,179)(188,211)(189,210)
(190,220)(191,219)(192,218)(193,217)(194,216)(195,215)(196,214)(197,213)
(198,212)(199,200)(201,209)(202,208)(203,207)(204,206)(221,288)(222,287)
(223,297)(224,296)(225,295)(226,294)(227,293)(228,292)(229,291)(230,290)
(231,289)(232,277)(233,276)(234,286)(235,285)(236,284)(237,283)(238,282)
(239,281)(240,280)(241,279)(242,278)(243,321)(244,320)(245,330)(246,329)
(247,328)(248,327)(249,326)(250,325)(251,324)(252,323)(253,322)(254,310)
(255,309)(256,319)(257,318)(258,317)(259,316)(260,315)(261,314)(262,313)
(263,312)(264,311)(265,299)(266,298)(267,308)(268,307)(269,306)(270,305)
(271,304)(272,303)(273,302)(274,301)(275,300);
s2 := Sym(330)!( 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)
( 56,166)( 57,167)( 58,168)( 59,169)( 60,170)( 61,171)( 62,172)( 63,173)
( 64,174)( 65,175)( 66,176)( 67,177)( 68,178)( 69,179)( 70,180)( 71,181)
( 72,182)( 73,183)( 74,184)( 75,185)( 76,186)( 77,187)( 78,188)( 79,189)
( 80,190)( 81,191)( 82,192)( 83,193)( 84,194)( 85,195)( 86,196)( 87,197)
( 88,198)( 89,199)( 90,200)( 91,201)( 92,202)( 93,203)( 94,204)( 95,205)
( 96,206)( 97,207)( 98,208)( 99,209)(100,210)(101,211)(102,212)(103,213)
(104,214)(105,215)(106,216)(107,217)(108,218)(109,219)(110,220)(111,276)
(112,277)(113,278)(114,279)(115,280)(116,281)(117,282)(118,283)(119,284)
(120,285)(121,286)(122,287)(123,288)(124,289)(125,290)(126,291)(127,292)
(128,293)(129,294)(130,295)(131,296)(132,297)(133,298)(134,299)(135,300)
(136,301)(137,302)(138,303)(139,304)(140,305)(141,306)(142,307)(143,308)
(144,309)(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)
(152,317)(153,318)(154,319)(155,320)(156,321)(157,322)(158,323)(159,324)
(160,325)(161,326)(162,327)(163,328)(164,329)(165,330);
poly := sub<Sym(330)|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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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