Overview
- Group
- SmallGroup(1248,506)
- Rank
- 3
- Schläfli Type
- {104,6}
- Vertices, edges, …
- 104, 312, 6
- Order of s0s1s2
- 312
- Order of s0s1s2s1
- 2
- Also known as
- {104,6|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
12-fold
13-fold
24-fold
26-fold
39-fold
52-fold
78-fold
104-fold
156-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
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.