Polytope of Type {6,104}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,104}*1248
Also Known As : {6,104|2}. if this polytope has another name.
Group : SmallGroup(1248,506)
Rank : 3
Schlafli Type : {6,104}
Number of vertices, edges, etc : 6, 312, 104
Order of s0s1s2 : 312
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 : {6,52}*624a
3-fold quotients : {2,104}*416
4-fold quotients : {6,26}*312
6-fold quotients : {2,52}*208
12-fold quotients : {2,26}*104
13-fold quotients : {6,8}*96
24-fold quotients : {2,13}*52
26-fold quotients : {6,4}*48a
39-fold quotients : {2,8}*32
52-fold quotients : {6,2}*24
78-fold quotients : {2,4}*16
104-fold quotients : {3,2}*12
156-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 14, 27)( 15, 28)( 16, 29)( 17, 30)( 18, 31)( 19, 32)( 20, 33)( 21, 34)
( 22, 35)( 23, 36)( 24, 37)( 25, 38)( 26, 39)( 53, 66)( 54, 67)( 55, 68)
( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)( 63, 76)
( 64, 77)( 65, 78)( 92,105)( 93,106)( 94,107)( 95,108)( 96,109)( 97,110)
( 98,111)( 99,112)(100,113)(101,114)(102,115)(103,116)(104,117)(131,144)
(132,145)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)(139,152)
(140,153)(141,154)(142,155)(143,156)(170,183)(171,184)(172,185)(173,186)
(174,187)(175,188)(176,189)(177,190)(178,191)(179,192)(180,193)(181,194)
(182,195)(209,222)(210,223)(211,224)(212,225)(213,226)(214,227)(215,228)
(216,229)(217,230)(218,231)(219,232)(220,233)(221,234)(248,261)(249,262)
(250,263)(251,264)(252,265)(253,266)(254,267)(255,268)(256,269)(257,270)
(258,271)(259,272)(260,273)(287,300)(288,301)(289,302)(290,303)(291,304)
(292,305)(293,306)(294,307)(295,308)(296,309)(297,310)(298,311)(299,312);;
s1 := ( 1, 14)( 2, 26)( 3, 25)( 4, 24)( 5, 23)( 6, 22)( 7, 21)( 8, 20)
( 9, 19)( 10, 18)( 11, 17)( 12, 16)( 13, 15)( 28, 39)( 29, 38)( 30, 37)
( 31, 36)( 32, 35)( 33, 34)( 40, 53)( 41, 65)( 42, 64)( 43, 63)( 44, 62)
( 45, 61)( 46, 60)( 47, 59)( 48, 58)( 49, 57)( 50, 56)( 51, 55)( 52, 54)
( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,131)( 80,143)
( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,137)( 87,136)( 88,135)
( 89,134)( 90,133)( 91,132)( 92,118)( 93,130)( 94,129)( 95,128)( 96,127)
( 97,126)( 98,125)( 99,124)(100,123)(101,122)(102,121)(103,120)(104,119)
(105,144)(106,156)(107,155)(108,154)(109,153)(110,152)(111,151)(112,150)
(113,149)(114,148)(115,147)(116,146)(117,145)(157,248)(158,260)(159,259)
(160,258)(161,257)(162,256)(163,255)(164,254)(165,253)(166,252)(167,251)
(168,250)(169,249)(170,235)(171,247)(172,246)(173,245)(174,244)(175,243)
(176,242)(177,241)(178,240)(179,239)(180,238)(181,237)(182,236)(183,261)
(184,273)(185,272)(186,271)(187,270)(188,269)(189,268)(190,267)(191,266)
(192,265)(193,264)(194,263)(195,262)(196,287)(197,299)(198,298)(199,297)
(200,296)(201,295)(202,294)(203,293)(204,292)(205,291)(206,290)(207,289)
(208,288)(209,274)(210,286)(211,285)(212,284)(213,283)(214,282)(215,281)
(216,280)(217,279)(218,278)(219,277)(220,276)(221,275)(222,300)(223,312)
(224,311)(225,310)(226,309)(227,308)(228,307)(229,306)(230,305)(231,304)
(232,303)(233,302)(234,301);;
s2 := ( 1,158)( 2,157)( 3,169)( 4,168)( 5,167)( 6,166)( 7,165)( 8,164)
( 9,163)( 10,162)( 11,161)( 12,160)( 13,159)( 14,171)( 15,170)( 16,182)
( 17,181)( 18,180)( 19,179)( 20,178)( 21,177)( 22,176)( 23,175)( 24,174)
( 25,173)( 26,172)( 27,184)( 28,183)( 29,195)( 30,194)( 31,193)( 32,192)
( 33,191)( 34,190)( 35,189)( 36,188)( 37,187)( 38,186)( 39,185)( 40,197)
( 41,196)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)( 48,202)
( 49,201)( 50,200)( 51,199)( 52,198)( 53,210)( 54,209)( 55,221)( 56,220)
( 57,219)( 58,218)( 59,217)( 60,216)( 61,215)( 62,214)( 63,213)( 64,212)
( 65,211)( 66,223)( 67,222)( 68,234)( 69,233)( 70,232)( 71,231)( 72,230)
( 73,229)( 74,228)( 75,227)( 76,226)( 77,225)( 78,224)( 79,275)( 80,274)
( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)( 88,279)
( 89,278)( 90,277)( 91,276)( 92,288)( 93,287)( 94,299)( 95,298)( 96,297)
( 97,296)( 98,295)( 99,294)(100,293)(101,292)(102,291)(103,290)(104,289)
(105,301)(106,300)(107,312)(108,311)(109,310)(110,309)(111,308)(112,307)
(113,306)(114,305)(115,304)(116,303)(117,302)(118,236)(119,235)(120,247)
(121,246)(122,245)(123,244)(124,243)(125,242)(126,241)(127,240)(128,239)
(129,238)(130,237)(131,249)(132,248)(133,260)(134,259)(135,258)(136,257)
(137,256)(138,255)(139,254)(140,253)(141,252)(142,251)(143,250)(144,262)
(145,261)(146,273)(147,272)(148,271)(149,270)(150,269)(151,268)(152,267)
(153,266)(154,265)(155,264)(156,263);;
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,
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*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(312)!( 14, 27)( 15, 28)( 16, 29)( 17, 30)( 18, 31)( 19, 32)( 20, 33)
( 21, 34)( 22, 35)( 23, 36)( 24, 37)( 25, 38)( 26, 39)( 53, 66)( 54, 67)
( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)
( 63, 76)( 64, 77)( 65, 78)( 92,105)( 93,106)( 94,107)( 95,108)( 96,109)
( 97,110)( 98,111)( 99,112)(100,113)(101,114)(102,115)(103,116)(104,117)
(131,144)(132,145)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)
(139,152)(140,153)(141,154)(142,155)(143,156)(170,183)(171,184)(172,185)
(173,186)(174,187)(175,188)(176,189)(177,190)(178,191)(179,192)(180,193)
(181,194)(182,195)(209,222)(210,223)(211,224)(212,225)(213,226)(214,227)
(215,228)(216,229)(217,230)(218,231)(219,232)(220,233)(221,234)(248,261)
(249,262)(250,263)(251,264)(252,265)(253,266)(254,267)(255,268)(256,269)
(257,270)(258,271)(259,272)(260,273)(287,300)(288,301)(289,302)(290,303)
(291,304)(292,305)(293,306)(294,307)(295,308)(296,309)(297,310)(298,311)
(299,312);
s1 := Sym(312)!( 1, 14)( 2, 26)( 3, 25)( 4, 24)( 5, 23)( 6, 22)( 7, 21)
( 8, 20)( 9, 19)( 10, 18)( 11, 17)( 12, 16)( 13, 15)( 28, 39)( 29, 38)
( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 40, 53)( 41, 65)( 42, 64)( 43, 63)
( 44, 62)( 45, 61)( 46, 60)( 47, 59)( 48, 58)( 49, 57)( 50, 56)( 51, 55)
( 52, 54)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,131)
( 80,143)( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,137)( 87,136)
( 88,135)( 89,134)( 90,133)( 91,132)( 92,118)( 93,130)( 94,129)( 95,128)
( 96,127)( 97,126)( 98,125)( 99,124)(100,123)(101,122)(102,121)(103,120)
(104,119)(105,144)(106,156)(107,155)(108,154)(109,153)(110,152)(111,151)
(112,150)(113,149)(114,148)(115,147)(116,146)(117,145)(157,248)(158,260)
(159,259)(160,258)(161,257)(162,256)(163,255)(164,254)(165,253)(166,252)
(167,251)(168,250)(169,249)(170,235)(171,247)(172,246)(173,245)(174,244)
(175,243)(176,242)(177,241)(178,240)(179,239)(180,238)(181,237)(182,236)
(183,261)(184,273)(185,272)(186,271)(187,270)(188,269)(189,268)(190,267)
(191,266)(192,265)(193,264)(194,263)(195,262)(196,287)(197,299)(198,298)
(199,297)(200,296)(201,295)(202,294)(203,293)(204,292)(205,291)(206,290)
(207,289)(208,288)(209,274)(210,286)(211,285)(212,284)(213,283)(214,282)
(215,281)(216,280)(217,279)(218,278)(219,277)(220,276)(221,275)(222,300)
(223,312)(224,311)(225,310)(226,309)(227,308)(228,307)(229,306)(230,305)
(231,304)(232,303)(233,302)(234,301);
s2 := Sym(312)!( 1,158)( 2,157)( 3,169)( 4,168)( 5,167)( 6,166)( 7,165)
( 8,164)( 9,163)( 10,162)( 11,161)( 12,160)( 13,159)( 14,171)( 15,170)
( 16,182)( 17,181)( 18,180)( 19,179)( 20,178)( 21,177)( 22,176)( 23,175)
( 24,174)( 25,173)( 26,172)( 27,184)( 28,183)( 29,195)( 30,194)( 31,193)
( 32,192)( 33,191)( 34,190)( 35,189)( 36,188)( 37,187)( 38,186)( 39,185)
( 40,197)( 41,196)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)
( 48,202)( 49,201)( 50,200)( 51,199)( 52,198)( 53,210)( 54,209)( 55,221)
( 56,220)( 57,219)( 58,218)( 59,217)( 60,216)( 61,215)( 62,214)( 63,213)
( 64,212)( 65,211)( 66,223)( 67,222)( 68,234)( 69,233)( 70,232)( 71,231)
( 72,230)( 73,229)( 74,228)( 75,227)( 76,226)( 77,225)( 78,224)( 79,275)
( 80,274)( 81,286)( 82,285)( 83,284)( 84,283)( 85,282)( 86,281)( 87,280)
( 88,279)( 89,278)( 90,277)( 91,276)( 92,288)( 93,287)( 94,299)( 95,298)
( 96,297)( 97,296)( 98,295)( 99,294)(100,293)(101,292)(102,291)(103,290)
(104,289)(105,301)(106,300)(107,312)(108,311)(109,310)(110,309)(111,308)
(112,307)(113,306)(114,305)(115,304)(116,303)(117,302)(118,236)(119,235)
(120,247)(121,246)(122,245)(123,244)(124,243)(125,242)(126,241)(127,240)
(128,239)(129,238)(130,237)(131,249)(132,248)(133,260)(134,259)(135,258)
(136,257)(137,256)(138,255)(139,254)(140,253)(141,252)(142,251)(143,250)
(144,262)(145,261)(146,273)(147,272)(148,271)(149,270)(150,269)(151,268)
(152,267)(153,266)(154,265)(155,264)(156,263);
poly := sub<Sym(312)|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,
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*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