Polytope of Type {102,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {102,6}*1224b
Also Known As : {102,6|2}. if this polytope has another name.
Group : SmallGroup(1224,156)
Rank : 3
Schlafli Type : {102,6}
Number of vertices, edges, etc : 102, 306, 6
Order of s0s1s2 : 102
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {34,6}*408, {102,2}*408
6-fold quotients : {51,2}*204
9-fold quotients : {34,2}*136
17-fold quotients : {6,6}*72a
18-fold quotients : {17,2}*68
51-fold quotients : {2,6}*24, {6,2}*24
102-fold quotients : {2,3}*12, {3,2}*12
153-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)( 9, 10)
( 18, 35)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 46)( 25, 45)
( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 39)( 32, 38)( 33, 37)
( 34, 36)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)
( 60, 61)( 69, 86)( 70,102)( 71,101)( 72,100)( 73, 99)( 74, 98)( 75, 97)
( 76, 96)( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81, 91)( 82, 90)( 83, 89)
( 84, 88)( 85, 87)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)
(110,113)(111,112)(120,137)(121,153)(122,152)(123,151)(124,150)(125,149)
(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)(132,142)(133,141)
(134,140)(135,139)(136,138)(155,170)(156,169)(157,168)(158,167)(159,166)
(160,165)(161,164)(162,163)(171,188)(172,204)(173,203)(174,202)(175,201)
(176,200)(177,199)(178,198)(179,197)(180,196)(181,195)(182,194)(183,193)
(184,192)(185,191)(186,190)(187,189)(206,221)(207,220)(208,219)(209,218)
(210,217)(211,216)(212,215)(213,214)(222,239)(223,255)(224,254)(225,253)
(226,252)(227,251)(228,250)(229,249)(230,248)(231,247)(232,246)(233,245)
(234,244)(235,243)(236,242)(237,241)(238,240)(257,272)(258,271)(259,270)
(260,269)(261,268)(262,267)(263,266)(264,265)(273,290)(274,306)(275,305)
(276,304)(277,303)(278,302)(279,301)(280,300)(281,299)(282,298)(283,297)
(284,296)(285,295)(286,294)(287,293)(288,292)(289,291);;
s1 := ( 1, 19)( 2, 18)( 3, 34)( 4, 33)( 5, 32)( 6, 31)( 7, 30)( 8, 29)
( 9, 28)( 10, 27)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)
( 17, 20)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 43, 45)( 52,121)( 53,120)( 54,136)( 55,135)( 56,134)( 57,133)( 58,132)
( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)( 64,126)( 65,125)( 66,124)
( 67,123)( 68,122)( 69,104)( 70,103)( 71,119)( 72,118)( 73,117)( 74,116)
( 75,115)( 76,114)( 77,113)( 78,112)( 79,111)( 80,110)( 81,109)( 82,108)
( 83,107)( 84,106)( 85,105)( 86,138)( 87,137)( 88,153)( 89,152)( 90,151)
( 91,150)( 92,149)( 93,148)( 94,147)( 95,146)( 96,145)( 97,144)( 98,143)
( 99,142)(100,141)(101,140)(102,139)(154,172)(155,171)(156,187)(157,186)
(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)
(166,177)(167,176)(168,175)(169,174)(170,173)(188,189)(190,204)(191,203)
(192,202)(193,201)(194,200)(195,199)(196,198)(205,274)(206,273)(207,289)
(208,288)(209,287)(210,286)(211,285)(212,284)(213,283)(214,282)(215,281)
(216,280)(217,279)(218,278)(219,277)(220,276)(221,275)(222,257)(223,256)
(224,272)(225,271)(226,270)(227,269)(228,268)(229,267)(230,266)(231,265)
(232,264)(233,263)(234,262)(235,261)(236,260)(237,259)(238,258)(239,291)
(240,290)(241,306)(242,305)(243,304)(244,303)(245,302)(246,301)(247,300)
(248,299)(249,298)(250,297)(251,296)(252,295)(253,294)(254,293)(255,292);;
s2 := ( 1,205)( 2,206)( 3,207)( 4,208)( 5,209)( 6,210)( 7,211)( 8,212)
( 9,213)( 10,214)( 11,215)( 12,216)( 13,217)( 14,218)( 15,219)( 16,220)
( 17,221)( 18,222)( 19,223)( 20,224)( 21,225)( 22,226)( 23,227)( 24,228)
( 25,229)( 26,230)( 27,231)( 28,232)( 29,233)( 30,234)( 31,235)( 32,236)
( 33,237)( 34,238)( 35,239)( 36,240)( 37,241)( 38,242)( 39,243)( 40,244)
( 41,245)( 42,246)( 43,247)( 44,248)( 45,249)( 46,250)( 47,251)( 48,252)
( 49,253)( 50,254)( 51,255)( 52,154)( 53,155)( 54,156)( 55,157)( 56,158)
( 57,159)( 58,160)( 59,161)( 60,162)( 61,163)( 62,164)( 63,165)( 64,166)
( 65,167)( 66,168)( 67,169)( 68,170)( 69,171)( 70,172)( 71,173)( 72,174)
( 73,175)( 74,176)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)( 80,182)
( 81,183)( 82,184)( 83,185)( 84,186)( 85,187)( 86,188)( 87,189)( 88,190)
( 89,191)( 90,192)( 91,193)( 92,194)( 93,195)( 94,196)( 95,197)( 96,198)
( 97,199)( 98,200)( 99,201)(100,202)(101,203)(102,204)(103,256)(104,257)
(105,258)(106,259)(107,260)(108,261)(109,262)(110,263)(111,264)(112,265)
(113,266)(114,267)(115,268)(116,269)(117,270)(118,271)(119,272)(120,273)
(121,274)(122,275)(123,276)(124,277)(125,278)(126,279)(127,280)(128,281)
(129,282)(130,283)(131,284)(132,285)(133,286)(134,287)(135,288)(136,289)
(137,290)(138,291)(139,292)(140,293)(141,294)(142,295)(143,296)(144,297)
(145,298)(146,299)(147,300)(148,301)(149,302)(150,303)(151,304)(152,305)
(153,306);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(306)!( 2, 17)( 3, 16)( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)
( 9, 10)( 18, 35)( 19, 51)( 20, 50)( 21, 49)( 22, 48)( 23, 47)( 24, 46)
( 25, 45)( 26, 44)( 27, 43)( 28, 42)( 29, 41)( 30, 40)( 31, 39)( 32, 38)
( 33, 37)( 34, 36)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)
( 59, 62)( 60, 61)( 69, 86)( 70,102)( 71,101)( 72,100)( 73, 99)( 74, 98)
( 75, 97)( 76, 96)( 77, 95)( 78, 94)( 79, 93)( 80, 92)( 81, 91)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)(104,119)(105,118)(106,117)(107,116)(108,115)
(109,114)(110,113)(111,112)(120,137)(121,153)(122,152)(123,151)(124,150)
(125,149)(126,148)(127,147)(128,146)(129,145)(130,144)(131,143)(132,142)
(133,141)(134,140)(135,139)(136,138)(155,170)(156,169)(157,168)(158,167)
(159,166)(160,165)(161,164)(162,163)(171,188)(172,204)(173,203)(174,202)
(175,201)(176,200)(177,199)(178,198)(179,197)(180,196)(181,195)(182,194)
(183,193)(184,192)(185,191)(186,190)(187,189)(206,221)(207,220)(208,219)
(209,218)(210,217)(211,216)(212,215)(213,214)(222,239)(223,255)(224,254)
(225,253)(226,252)(227,251)(228,250)(229,249)(230,248)(231,247)(232,246)
(233,245)(234,244)(235,243)(236,242)(237,241)(238,240)(257,272)(258,271)
(259,270)(260,269)(261,268)(262,267)(263,266)(264,265)(273,290)(274,306)
(275,305)(276,304)(277,303)(278,302)(279,301)(280,300)(281,299)(282,298)
(283,297)(284,296)(285,295)(286,294)(287,293)(288,292)(289,291);
s1 := Sym(306)!( 1, 19)( 2, 18)( 3, 34)( 4, 33)( 5, 32)( 6, 31)( 7, 30)
( 8, 29)( 9, 28)( 10, 27)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)
( 16, 21)( 17, 20)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)
( 42, 46)( 43, 45)( 52,121)( 53,120)( 54,136)( 55,135)( 56,134)( 57,133)
( 58,132)( 59,131)( 60,130)( 61,129)( 62,128)( 63,127)( 64,126)( 65,125)
( 66,124)( 67,123)( 68,122)( 69,104)( 70,103)( 71,119)( 72,118)( 73,117)
( 74,116)( 75,115)( 76,114)( 77,113)( 78,112)( 79,111)( 80,110)( 81,109)
( 82,108)( 83,107)( 84,106)( 85,105)( 86,138)( 87,137)( 88,153)( 89,152)
( 90,151)( 91,150)( 92,149)( 93,148)( 94,147)( 95,146)( 96,145)( 97,144)
( 98,143)( 99,142)(100,141)(101,140)(102,139)(154,172)(155,171)(156,187)
(157,186)(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)
(165,178)(166,177)(167,176)(168,175)(169,174)(170,173)(188,189)(190,204)
(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)(205,274)(206,273)
(207,289)(208,288)(209,287)(210,286)(211,285)(212,284)(213,283)(214,282)
(215,281)(216,280)(217,279)(218,278)(219,277)(220,276)(221,275)(222,257)
(223,256)(224,272)(225,271)(226,270)(227,269)(228,268)(229,267)(230,266)
(231,265)(232,264)(233,263)(234,262)(235,261)(236,260)(237,259)(238,258)
(239,291)(240,290)(241,306)(242,305)(243,304)(244,303)(245,302)(246,301)
(247,300)(248,299)(249,298)(250,297)(251,296)(252,295)(253,294)(254,293)
(255,292);
s2 := Sym(306)!( 1,205)( 2,206)( 3,207)( 4,208)( 5,209)( 6,210)( 7,211)
( 8,212)( 9,213)( 10,214)( 11,215)( 12,216)( 13,217)( 14,218)( 15,219)
( 16,220)( 17,221)( 18,222)( 19,223)( 20,224)( 21,225)( 22,226)( 23,227)
( 24,228)( 25,229)( 26,230)( 27,231)( 28,232)( 29,233)( 30,234)( 31,235)
( 32,236)( 33,237)( 34,238)( 35,239)( 36,240)( 37,241)( 38,242)( 39,243)
( 40,244)( 41,245)( 42,246)( 43,247)( 44,248)( 45,249)( 46,250)( 47,251)
( 48,252)( 49,253)( 50,254)( 51,255)( 52,154)( 53,155)( 54,156)( 55,157)
( 56,158)( 57,159)( 58,160)( 59,161)( 60,162)( 61,163)( 62,164)( 63,165)
( 64,166)( 65,167)( 66,168)( 67,169)( 68,170)( 69,171)( 70,172)( 71,173)
( 72,174)( 73,175)( 74,176)( 75,177)( 76,178)( 77,179)( 78,180)( 79,181)
( 80,182)( 81,183)( 82,184)( 83,185)( 84,186)( 85,187)( 86,188)( 87,189)
( 88,190)( 89,191)( 90,192)( 91,193)( 92,194)( 93,195)( 94,196)( 95,197)
( 96,198)( 97,199)( 98,200)( 99,201)(100,202)(101,203)(102,204)(103,256)
(104,257)(105,258)(106,259)(107,260)(108,261)(109,262)(110,263)(111,264)
(112,265)(113,266)(114,267)(115,268)(116,269)(117,270)(118,271)(119,272)
(120,273)(121,274)(122,275)(123,276)(124,277)(125,278)(126,279)(127,280)
(128,281)(129,282)(130,283)(131,284)(132,285)(133,286)(134,287)(135,288)
(136,289)(137,290)(138,291)(139,292)(140,293)(141,294)(142,295)(143,296)
(144,297)(145,298)(146,299)(147,300)(148,301)(149,302)(150,303)(151,304)
(152,305)(153,306);
poly := sub<Sym(306)|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 >;
References : None.
to this polytope