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