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