Polytope of Type {26,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,24}*1248
Also Known As : {26,24|2}. if this polytope has another name.
Group : SmallGroup(1248,501)
Rank : 3
Schlafli Type : {26,24}
Number of vertices, edges, etc : 26, 312, 24
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 : {26,12}*624
3-fold quotients : {26,8}*416
4-fold quotients : {26,6}*312
6-fold quotients : {26,4}*208
12-fold quotients : {26,2}*104
13-fold quotients : {2,24}*96
24-fold quotients : {13,2}*52
26-fold quotients : {2,12}*48
39-fold quotients : {2,8}*32
52-fold quotients : {2,6}*24
78-fold quotients : {2,4}*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)( 80, 91)( 81, 90)( 82, 89)( 83, 88)
( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)
(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(119,130)(120,129)
(121,128)(122,127)(123,126)(124,125)(132,143)(133,142)(134,141)(135,140)
(136,139)(137,138)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)
(158,169)(159,168)(160,167)(161,166)(162,165)(163,164)(171,182)(172,181)
(173,180)(174,179)(175,178)(176,177)(184,195)(185,194)(186,193)(187,192)
(188,191)(189,190)(197,208)(198,207)(199,206)(200,205)(201,204)(202,203)
(210,221)(211,220)(212,219)(213,218)(214,217)(215,216)(223,234)(224,233)
(225,232)(226,231)(227,230)(228,229)(236,247)(237,246)(238,245)(239,244)
(240,243)(241,242)(249,260)(250,259)(251,258)(252,257)(253,256)(254,255)
(262,273)(263,272)(264,271)(265,270)(266,269)(267,268)(275,286)(276,285)
(277,284)(278,283)(279,282)(280,281)(288,299)(289,298)(290,297)(291,296)
(292,295)(293,294)(301,312)(302,311)(303,310)(304,309)(305,308)(306,307);;
s1 := ( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 28)( 15, 27)
( 16, 39)( 17, 38)( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)( 23, 32)
( 24, 31)( 25, 30)( 26, 29)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)
( 46, 48)( 53, 67)( 54, 66)( 55, 78)( 56, 77)( 57, 76)( 58, 75)( 59, 74)
( 60, 73)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)( 79,119)( 80,118)
( 81,130)( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)( 88,123)
( 89,122)( 90,121)( 91,120)( 92,145)( 93,144)( 94,156)( 95,155)( 96,154)
( 97,153)( 98,152)( 99,151)(100,150)(101,149)(102,148)(103,147)(104,146)
(105,132)(106,131)(107,143)(108,142)(109,141)(110,140)(111,139)(112,138)
(113,137)(114,136)(115,135)(116,134)(117,133)(157,236)(158,235)(159,247)
(160,246)(161,245)(162,244)(163,243)(164,242)(165,241)(166,240)(167,239)
(168,238)(169,237)(170,262)(171,261)(172,273)(173,272)(174,271)(175,270)
(176,269)(177,268)(178,267)(179,266)(180,265)(181,264)(182,263)(183,249)
(184,248)(185,260)(186,259)(187,258)(188,257)(189,256)(190,255)(191,254)
(192,253)(193,252)(194,251)(195,250)(196,275)(197,274)(198,286)(199,285)
(200,284)(201,283)(202,282)(203,281)(204,280)(205,279)(206,278)(207,277)
(208,276)(209,301)(210,300)(211,312)(212,311)(213,310)(214,309)(215,308)
(216,307)(217,306)(218,305)(219,304)(220,303)(221,302)(222,288)(223,287)
(224,299)(225,298)(226,297)(227,296)(228,295)(229,294)(230,293)(231,292)
(232,291)(233,290)(234,289);;
s2 := ( 1,170)( 2,171)( 3,172)( 4,173)( 5,174)( 6,175)( 7,176)( 8,177)
( 9,178)( 10,179)( 11,180)( 12,181)( 13,182)( 14,157)( 15,158)( 16,159)
( 17,160)( 18,161)( 19,162)( 20,163)( 21,164)( 22,165)( 23,166)( 24,167)
( 25,168)( 26,169)( 27,183)( 28,184)( 29,185)( 30,186)( 31,187)( 32,188)
( 33,189)( 34,190)( 35,191)( 36,192)( 37,193)( 38,194)( 39,195)( 40,209)
( 41,210)( 42,211)( 43,212)( 44,213)( 45,214)( 46,215)( 47,216)( 48,217)
( 49,218)( 50,219)( 51,220)( 52,221)( 53,196)( 54,197)( 55,198)( 56,199)
( 57,200)( 58,201)( 59,202)( 60,203)( 61,204)( 62,205)( 63,206)( 64,207)
( 65,208)( 66,222)( 67,223)( 68,224)( 69,225)( 70,226)( 71,227)( 72,228)
( 73,229)( 74,230)( 75,231)( 76,232)( 77,233)( 78,234)( 79,287)( 80,288)
( 81,289)( 82,290)( 83,291)( 84,292)( 85,293)( 86,294)( 87,295)( 88,296)
( 89,297)( 90,298)( 91,299)( 92,274)( 93,275)( 94,276)( 95,277)( 96,278)
( 97,279)( 98,280)( 99,281)(100,282)(101,283)(102,284)(103,285)(104,286)
(105,300)(106,301)(107,302)(108,303)(109,304)(110,305)(111,306)(112,307)
(113,308)(114,309)(115,310)(116,311)(117,312)(118,248)(119,249)(120,250)
(121,251)(122,252)(123,253)(124,254)(125,255)(126,256)(127,257)(128,258)
(129,259)(130,260)(131,235)(132,236)(133,237)(134,238)(135,239)(136,240)
(137,241)(138,242)(139,243)(140,244)(141,245)(142,246)(143,247)(144,261)
(145,262)(146,263)(147,264)(148,265)(149,266)(150,267)(151,268)(152,269)
(153,270)(154,271)(155,272)(156,273);;
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
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)( 80, 91)( 81, 90)( 82, 89)
( 83, 88)( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)
( 98, 99)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(119,130)
(120,129)(121,128)(122,127)(123,126)(124,125)(132,143)(133,142)(134,141)
(135,140)(136,139)(137,138)(145,156)(146,155)(147,154)(148,153)(149,152)
(150,151)(158,169)(159,168)(160,167)(161,166)(162,165)(163,164)(171,182)
(172,181)(173,180)(174,179)(175,178)(176,177)(184,195)(185,194)(186,193)
(187,192)(188,191)(189,190)(197,208)(198,207)(199,206)(200,205)(201,204)
(202,203)(210,221)(211,220)(212,219)(213,218)(214,217)(215,216)(223,234)
(224,233)(225,232)(226,231)(227,230)(228,229)(236,247)(237,246)(238,245)
(239,244)(240,243)(241,242)(249,260)(250,259)(251,258)(252,257)(253,256)
(254,255)(262,273)(263,272)(264,271)(265,270)(266,269)(267,268)(275,286)
(276,285)(277,284)(278,283)(279,282)(280,281)(288,299)(289,298)(290,297)
(291,296)(292,295)(293,294)(301,312)(302,311)(303,310)(304,309)(305,308)
(306,307);
s1 := Sym(312)!( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 28)
( 15, 27)( 16, 39)( 17, 38)( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)
( 23, 32)( 24, 31)( 25, 30)( 26, 29)( 40, 41)( 42, 52)( 43, 51)( 44, 50)
( 45, 49)( 46, 48)( 53, 67)( 54, 66)( 55, 78)( 56, 77)( 57, 76)( 58, 75)
( 59, 74)( 60, 73)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)( 79,119)
( 80,118)( 81,130)( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)
( 88,123)( 89,122)( 90,121)( 91,120)( 92,145)( 93,144)( 94,156)( 95,155)
( 96,154)( 97,153)( 98,152)( 99,151)(100,150)(101,149)(102,148)(103,147)
(104,146)(105,132)(106,131)(107,143)(108,142)(109,141)(110,140)(111,139)
(112,138)(113,137)(114,136)(115,135)(116,134)(117,133)(157,236)(158,235)
(159,247)(160,246)(161,245)(162,244)(163,243)(164,242)(165,241)(166,240)
(167,239)(168,238)(169,237)(170,262)(171,261)(172,273)(173,272)(174,271)
(175,270)(176,269)(177,268)(178,267)(179,266)(180,265)(181,264)(182,263)
(183,249)(184,248)(185,260)(186,259)(187,258)(188,257)(189,256)(190,255)
(191,254)(192,253)(193,252)(194,251)(195,250)(196,275)(197,274)(198,286)
(199,285)(200,284)(201,283)(202,282)(203,281)(204,280)(205,279)(206,278)
(207,277)(208,276)(209,301)(210,300)(211,312)(212,311)(213,310)(214,309)
(215,308)(216,307)(217,306)(218,305)(219,304)(220,303)(221,302)(222,288)
(223,287)(224,299)(225,298)(226,297)(227,296)(228,295)(229,294)(230,293)
(231,292)(232,291)(233,290)(234,289);
s2 := Sym(312)!( 1,170)( 2,171)( 3,172)( 4,173)( 5,174)( 6,175)( 7,176)
( 8,177)( 9,178)( 10,179)( 11,180)( 12,181)( 13,182)( 14,157)( 15,158)
( 16,159)( 17,160)( 18,161)( 19,162)( 20,163)( 21,164)( 22,165)( 23,166)
( 24,167)( 25,168)( 26,169)( 27,183)( 28,184)( 29,185)( 30,186)( 31,187)
( 32,188)( 33,189)( 34,190)( 35,191)( 36,192)( 37,193)( 38,194)( 39,195)
( 40,209)( 41,210)( 42,211)( 43,212)( 44,213)( 45,214)( 46,215)( 47,216)
( 48,217)( 49,218)( 50,219)( 51,220)( 52,221)( 53,196)( 54,197)( 55,198)
( 56,199)( 57,200)( 58,201)( 59,202)( 60,203)( 61,204)( 62,205)( 63,206)
( 64,207)( 65,208)( 66,222)( 67,223)( 68,224)( 69,225)( 70,226)( 71,227)
( 72,228)( 73,229)( 74,230)( 75,231)( 76,232)( 77,233)( 78,234)( 79,287)
( 80,288)( 81,289)( 82,290)( 83,291)( 84,292)( 85,293)( 86,294)( 87,295)
( 88,296)( 89,297)( 90,298)( 91,299)( 92,274)( 93,275)( 94,276)( 95,277)
( 96,278)( 97,279)( 98,280)( 99,281)(100,282)(101,283)(102,284)(103,285)
(104,286)(105,300)(106,301)(107,302)(108,303)(109,304)(110,305)(111,306)
(112,307)(113,308)(114,309)(115,310)(116,311)(117,312)(118,248)(119,249)
(120,250)(121,251)(122,252)(123,253)(124,254)(125,255)(126,256)(127,257)
(128,258)(129,259)(130,260)(131,235)(132,236)(133,237)(134,238)(135,239)
(136,240)(137,241)(138,242)(139,243)(140,244)(141,245)(142,246)(143,247)
(144,261)(145,262)(146,263)(147,264)(148,265)(149,266)(150,267)(151,268)
(152,269)(153,270)(154,271)(155,272)(156,273);
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope