Polytope of Type {66,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {66,10}*1320
Also Known As : {66,10|2}. if this polytope has another name.
Group : SmallGroup(1320,170)
Rank : 3
Schlafli Type : {66,10}
Number of vertices, edges, etc : 66, 330, 10
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 : {22,10}*440
5-fold quotients : {66,2}*264
10-fold quotients : {33,2}*132
11-fold quotients : {6,10}*120
15-fold quotients : {22,2}*88
30-fold quotients : {11,2}*44
33-fold quotients : {2,10}*40
55-fold quotients : {6,2}*24
66-fold quotients : {2,5}*20
110-fold quotients : {3,2}*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)( 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)( 56,111)( 57,121)( 58,120)( 59,119)( 60,118)( 61,117)( 62,116)
( 63,115)( 64,114)( 65,113)( 66,112)( 67,122)( 68,132)( 69,131)( 70,130)
( 71,129)( 72,128)( 73,127)( 74,126)( 75,125)( 76,124)( 77,123)( 78,133)
( 79,143)( 80,142)( 81,141)( 82,140)( 83,139)( 84,138)( 85,137)( 86,136)
( 87,135)( 88,134)( 89,144)( 90,154)( 91,153)( 92,152)( 93,151)( 94,150)
( 95,149)( 96,148)( 97,147)( 98,146)( 99,145)(100,155)(101,165)(102,164)
(103,163)(104,162)(105,161)(106,160)(107,159)(108,158)(109,157)(110,156)
(167,176)(168,175)(169,174)(170,173)(171,172)(178,187)(179,186)(180,185)
(181,184)(182,183)(189,198)(190,197)(191,196)(192,195)(193,194)(200,209)
(201,208)(202,207)(203,206)(204,205)(211,220)(212,219)(213,218)(214,217)
(215,216)(221,276)(222,286)(223,285)(224,284)(225,283)(226,282)(227,281)
(228,280)(229,279)(230,278)(231,277)(232,287)(233,297)(234,296)(235,295)
(236,294)(237,293)(238,292)(239,291)(240,290)(241,289)(242,288)(243,298)
(244,308)(245,307)(246,306)(247,305)(248,304)(249,303)(250,302)(251,301)
(252,300)(253,299)(254,309)(255,319)(256,318)(257,317)(258,316)(259,315)
(260,314)(261,313)(262,312)(263,311)(264,310)(265,320)(266,330)(267,329)
(268,328)(269,327)(270,326)(271,325)(272,324)(273,323)(274,322)(275,321);;
s1 := ( 1, 57)( 2, 56)( 3, 66)( 4, 65)( 5, 64)( 6, 63)( 7, 62)( 8, 61)
( 9, 60)( 10, 59)( 11, 58)( 12,101)( 13,100)( 14,110)( 15,109)( 16,108)
( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23, 90)( 24, 89)
( 25, 99)( 26, 98)( 27, 97)( 28, 96)( 29, 95)( 30, 94)( 31, 93)( 32, 92)
( 33, 91)( 34, 79)( 35, 78)( 36, 88)( 37, 87)( 38, 86)( 39, 85)( 40, 84)
( 41, 83)( 42, 82)( 43, 81)( 44, 80)( 45, 68)( 46, 67)( 47, 77)( 48, 76)
( 49, 75)( 50, 74)( 51, 73)( 52, 72)( 53, 71)( 54, 70)( 55, 69)(111,112)
(113,121)(114,120)(115,119)(116,118)(122,156)(123,155)(124,165)(125,164)
(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)(133,145)
(134,144)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)
(142,147)(143,146)(166,222)(167,221)(168,231)(169,230)(170,229)(171,228)
(172,227)(173,226)(174,225)(175,224)(176,223)(177,266)(178,265)(179,275)
(180,274)(181,273)(182,272)(183,271)(184,270)(185,269)(186,268)(187,267)
(188,255)(189,254)(190,264)(191,263)(192,262)(193,261)(194,260)(195,259)
(196,258)(197,257)(198,256)(199,244)(200,243)(201,253)(202,252)(203,251)
(204,250)(205,249)(206,248)(207,247)(208,246)(209,245)(210,233)(211,232)
(212,242)(213,241)(214,240)(215,239)(216,238)(217,237)(218,236)(219,235)
(220,234)(276,277)(278,286)(279,285)(280,284)(281,283)(287,321)(288,320)
(289,330)(290,329)(291,328)(292,327)(293,326)(294,325)(295,324)(296,323)
(297,322)(298,310)(299,309)(300,319)(301,318)(302,317)(303,316)(304,315)
(305,314)(306,313)(307,312)(308,311);;
s2 := ( 1,177)( 2,178)( 3,179)( 4,180)( 5,181)( 6,182)( 7,183)( 8,184)
( 9,185)( 10,186)( 11,187)( 12,166)( 13,167)( 14,168)( 15,169)( 16,170)
( 17,171)( 18,172)( 19,173)( 20,174)( 21,175)( 22,176)( 23,210)( 24,211)
( 25,212)( 26,213)( 27,214)( 28,215)( 29,216)( 30,217)( 31,218)( 32,219)
( 33,220)( 34,199)( 35,200)( 36,201)( 37,202)( 38,203)( 39,204)( 40,205)
( 41,206)( 42,207)( 43,208)( 44,209)( 45,188)( 46,189)( 47,190)( 48,191)
( 49,192)( 50,193)( 51,194)( 52,195)( 53,196)( 54,197)( 55,198)( 56,232)
( 57,233)( 58,234)( 59,235)( 60,236)( 61,237)( 62,238)( 63,239)( 64,240)
( 65,241)( 66,242)( 67,221)( 68,222)( 69,223)( 70,224)( 71,225)( 72,226)
( 73,227)( 74,228)( 75,229)( 76,230)( 77,231)( 78,265)( 79,266)( 80,267)
( 81,268)( 82,269)( 83,270)( 84,271)( 85,272)( 86,273)( 87,274)( 88,275)
( 89,254)( 90,255)( 91,256)( 92,257)( 93,258)( 94,259)( 95,260)( 96,261)
( 97,262)( 98,263)( 99,264)(100,243)(101,244)(102,245)(103,246)(104,247)
(105,248)(106,249)(107,250)(108,251)(109,252)(110,253)(111,287)(112,288)
(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)(120,296)
(121,297)(122,276)(123,277)(124,278)(125,279)(126,280)(127,281)(128,282)
(129,283)(130,284)(131,285)(132,286)(133,320)(134,321)(135,322)(136,323)
(137,324)(138,325)(139,326)(140,327)(141,328)(142,329)(143,330)(144,309)
(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)(152,317)
(153,318)(154,319)(155,298)(156,299)(157,300)(158,301)(159,302)(160,303)
(161,304)(162,305)(163,306)(164,307)(165,308);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(330)!( 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)( 56,111)( 57,121)( 58,120)( 59,119)( 60,118)( 61,117)
( 62,116)( 63,115)( 64,114)( 65,113)( 66,112)( 67,122)( 68,132)( 69,131)
( 70,130)( 71,129)( 72,128)( 73,127)( 74,126)( 75,125)( 76,124)( 77,123)
( 78,133)( 79,143)( 80,142)( 81,141)( 82,140)( 83,139)( 84,138)( 85,137)
( 86,136)( 87,135)( 88,134)( 89,144)( 90,154)( 91,153)( 92,152)( 93,151)
( 94,150)( 95,149)( 96,148)( 97,147)( 98,146)( 99,145)(100,155)(101,165)
(102,164)(103,163)(104,162)(105,161)(106,160)(107,159)(108,158)(109,157)
(110,156)(167,176)(168,175)(169,174)(170,173)(171,172)(178,187)(179,186)
(180,185)(181,184)(182,183)(189,198)(190,197)(191,196)(192,195)(193,194)
(200,209)(201,208)(202,207)(203,206)(204,205)(211,220)(212,219)(213,218)
(214,217)(215,216)(221,276)(222,286)(223,285)(224,284)(225,283)(226,282)
(227,281)(228,280)(229,279)(230,278)(231,277)(232,287)(233,297)(234,296)
(235,295)(236,294)(237,293)(238,292)(239,291)(240,290)(241,289)(242,288)
(243,298)(244,308)(245,307)(246,306)(247,305)(248,304)(249,303)(250,302)
(251,301)(252,300)(253,299)(254,309)(255,319)(256,318)(257,317)(258,316)
(259,315)(260,314)(261,313)(262,312)(263,311)(264,310)(265,320)(266,330)
(267,329)(268,328)(269,327)(270,326)(271,325)(272,324)(273,323)(274,322)
(275,321);
s1 := Sym(330)!( 1, 57)( 2, 56)( 3, 66)( 4, 65)( 5, 64)( 6, 63)( 7, 62)
( 8, 61)( 9, 60)( 10, 59)( 11, 58)( 12,101)( 13,100)( 14,110)( 15,109)
( 16,108)( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23, 90)
( 24, 89)( 25, 99)( 26, 98)( 27, 97)( 28, 96)( 29, 95)( 30, 94)( 31, 93)
( 32, 92)( 33, 91)( 34, 79)( 35, 78)( 36, 88)( 37, 87)( 38, 86)( 39, 85)
( 40, 84)( 41, 83)( 42, 82)( 43, 81)( 44, 80)( 45, 68)( 46, 67)( 47, 77)
( 48, 76)( 49, 75)( 50, 74)( 51, 73)( 52, 72)( 53, 71)( 54, 70)( 55, 69)
(111,112)(113,121)(114,120)(115,119)(116,118)(122,156)(123,155)(124,165)
(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157)
(133,145)(134,144)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)
(141,148)(142,147)(143,146)(166,222)(167,221)(168,231)(169,230)(170,229)
(171,228)(172,227)(173,226)(174,225)(175,224)(176,223)(177,266)(178,265)
(179,275)(180,274)(181,273)(182,272)(183,271)(184,270)(185,269)(186,268)
(187,267)(188,255)(189,254)(190,264)(191,263)(192,262)(193,261)(194,260)
(195,259)(196,258)(197,257)(198,256)(199,244)(200,243)(201,253)(202,252)
(203,251)(204,250)(205,249)(206,248)(207,247)(208,246)(209,245)(210,233)
(211,232)(212,242)(213,241)(214,240)(215,239)(216,238)(217,237)(218,236)
(219,235)(220,234)(276,277)(278,286)(279,285)(280,284)(281,283)(287,321)
(288,320)(289,330)(290,329)(291,328)(292,327)(293,326)(294,325)(295,324)
(296,323)(297,322)(298,310)(299,309)(300,319)(301,318)(302,317)(303,316)
(304,315)(305,314)(306,313)(307,312)(308,311);
s2 := Sym(330)!( 1,177)( 2,178)( 3,179)( 4,180)( 5,181)( 6,182)( 7,183)
( 8,184)( 9,185)( 10,186)( 11,187)( 12,166)( 13,167)( 14,168)( 15,169)
( 16,170)( 17,171)( 18,172)( 19,173)( 20,174)( 21,175)( 22,176)( 23,210)
( 24,211)( 25,212)( 26,213)( 27,214)( 28,215)( 29,216)( 30,217)( 31,218)
( 32,219)( 33,220)( 34,199)( 35,200)( 36,201)( 37,202)( 38,203)( 39,204)
( 40,205)( 41,206)( 42,207)( 43,208)( 44,209)( 45,188)( 46,189)( 47,190)
( 48,191)( 49,192)( 50,193)( 51,194)( 52,195)( 53,196)( 54,197)( 55,198)
( 56,232)( 57,233)( 58,234)( 59,235)( 60,236)( 61,237)( 62,238)( 63,239)
( 64,240)( 65,241)( 66,242)( 67,221)( 68,222)( 69,223)( 70,224)( 71,225)
( 72,226)( 73,227)( 74,228)( 75,229)( 76,230)( 77,231)( 78,265)( 79,266)
( 80,267)( 81,268)( 82,269)( 83,270)( 84,271)( 85,272)( 86,273)( 87,274)
( 88,275)( 89,254)( 90,255)( 91,256)( 92,257)( 93,258)( 94,259)( 95,260)
( 96,261)( 97,262)( 98,263)( 99,264)(100,243)(101,244)(102,245)(103,246)
(104,247)(105,248)(106,249)(107,250)(108,251)(109,252)(110,253)(111,287)
(112,288)(113,289)(114,290)(115,291)(116,292)(117,293)(118,294)(119,295)
(120,296)(121,297)(122,276)(123,277)(124,278)(125,279)(126,280)(127,281)
(128,282)(129,283)(130,284)(131,285)(132,286)(133,320)(134,321)(135,322)
(136,323)(137,324)(138,325)(139,326)(140,327)(141,328)(142,329)(143,330)
(144,309)(145,310)(146,311)(147,312)(148,313)(149,314)(150,315)(151,316)
(152,317)(153,318)(154,319)(155,298)(156,299)(157,300)(158,301)(159,302)
(160,303)(161,304)(162,305)(163,306)(164,307)(165,308);
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*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 >;
References : None.
to this polytope