Polytope of Type {24,26}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,26}*1248
Also Known As : {24,26|2}. if this polytope has another name.
Group : SmallGroup(1248,501)
Rank : 3
Schlafli Type : {24,26}
Number of vertices, edges, etc : 24, 312, 26
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 : {12,26}*624
3-fold quotients : {8,26}*416
4-fold quotients : {6,26}*312
6-fold quotients : {4,26}*208
12-fold quotients : {2,26}*104
13-fold quotients : {24,2}*96
24-fold quotients : {2,13}*52
26-fold quotients : {12,2}*48
39-fold quotients : {8,2}*32
52-fold quotients : {6,2}*24
78-fold quotients : {4,2}*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)( 79,118)( 80,119)( 81,120)( 82,121)( 83,122)( 84,123)
( 85,124)( 86,125)( 87,126)( 88,127)( 89,128)( 90,129)( 91,130)( 92,144)
( 93,145)( 94,146)( 95,147)( 96,148)( 97,149)( 98,150)( 99,151)(100,152)
(101,153)(102,154)(103,155)(104,156)(105,131)(106,132)(107,133)(108,134)
(109,135)(110,136)(111,137)(112,138)(113,139)(114,140)(115,141)(116,142)
(117,143)(157,235)(158,236)(159,237)(160,238)(161,239)(162,240)(163,241)
(164,242)(165,243)(166,244)(167,245)(168,246)(169,247)(170,261)(171,262)
(172,263)(173,264)(174,265)(175,266)(176,267)(177,268)(178,269)(179,270)
(180,271)(181,272)(182,273)(183,248)(184,249)(185,250)(186,251)(187,252)
(188,253)(189,254)(190,255)(191,256)(192,257)(193,258)(194,259)(195,260)
(196,274)(197,275)(198,276)(199,277)(200,278)(201,279)(202,280)(203,281)
(204,282)(205,283)(206,284)(207,285)(208,286)(209,300)(210,301)(211,302)
(212,303)(213,304)(214,305)(215,306)(216,307)(217,308)(218,309)(219,310)
(220,311)(221,312)(222,287)(223,288)(224,289)(225,290)(226,291)(227,292)
(228,293)(229,294)(230,295)(231,296)(232,297)(233,298)(234,299);;
s1 := ( 1,170)( 2,182)( 3,181)( 4,180)( 5,179)( 6,178)( 7,177)( 8,176)
( 9,175)( 10,174)( 11,173)( 12,172)( 13,171)( 14,157)( 15,169)( 16,168)
( 17,167)( 18,166)( 19,165)( 20,164)( 21,163)( 22,162)( 23,161)( 24,160)
( 25,159)( 26,158)( 27,183)( 28,195)( 29,194)( 30,193)( 31,192)( 32,191)
( 33,190)( 34,189)( 35,188)( 36,187)( 37,186)( 38,185)( 39,184)( 40,209)
( 41,221)( 42,220)( 43,219)( 44,218)( 45,217)( 46,216)( 47,215)( 48,214)
( 49,213)( 50,212)( 51,211)( 52,210)( 53,196)( 54,208)( 55,207)( 56,206)
( 57,205)( 58,204)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)( 64,198)
( 65,197)( 66,222)( 67,234)( 68,233)( 69,232)( 70,231)( 71,230)( 72,229)
( 73,228)( 74,227)( 75,226)( 76,225)( 77,224)( 78,223)( 79,287)( 80,299)
( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)( 88,291)
( 89,290)( 90,289)( 91,288)( 92,274)( 93,286)( 94,285)( 95,284)( 96,283)
( 97,282)( 98,281)( 99,280)(100,279)(101,278)(102,277)(103,276)(104,275)
(105,300)(106,312)(107,311)(108,310)(109,309)(110,308)(111,307)(112,306)
(113,305)(114,304)(115,303)(116,302)(117,301)(118,248)(119,260)(120,259)
(121,258)(122,257)(123,256)(124,255)(125,254)(126,253)(127,252)(128,251)
(129,250)(130,249)(131,235)(132,247)(133,246)(134,245)(135,244)(136,243)
(137,242)(138,241)(139,240)(140,239)(141,238)(142,237)(143,236)(144,261)
(145,273)(146,272)(147,271)(148,270)(149,269)(150,268)(151,267)(152,266)
(153,265)(154,264)(155,263)(156,262);;
s2 := ( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 15)( 16, 26)
( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 28)( 29, 39)( 30, 38)( 31, 37)
( 32, 36)( 33, 35)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)( 46, 48)
( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)( 68, 78)
( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 80)( 81, 91)( 82, 90)( 83, 89)
( 84, 88)( 85, 87)( 92, 93)( 94,104)( 95,103)( 96,102)( 97,101)( 98,100)
(105,106)(107,117)(108,116)(109,115)(110,114)(111,113)(118,119)(120,130)
(121,129)(122,128)(123,127)(124,126)(131,132)(133,143)(134,142)(135,141)
(136,140)(137,139)(144,145)(146,156)(147,155)(148,154)(149,153)(150,152)
(157,158)(159,169)(160,168)(161,167)(162,166)(163,165)(170,171)(172,182)
(173,181)(174,180)(175,179)(176,178)(183,184)(185,195)(186,194)(187,193)
(188,192)(189,191)(196,197)(198,208)(199,207)(200,206)(201,205)(202,204)
(209,210)(211,221)(212,220)(213,219)(214,218)(215,217)(222,223)(224,234)
(225,233)(226,232)(227,231)(228,230)(235,236)(237,247)(238,246)(239,245)
(240,244)(241,243)(248,249)(250,260)(251,259)(252,258)(253,257)(254,256)
(261,262)(263,273)(264,272)(265,271)(266,270)(267,269)(274,275)(276,286)
(277,285)(278,284)(279,283)(280,282)(287,288)(289,299)(290,298)(291,297)
(292,296)(293,295)(300,301)(302,312)(303,311)(304,310)(305,309)(306,308);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 ];;
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)( 79,118)( 80,119)( 81,120)( 82,121)( 83,122)
( 84,123)( 85,124)( 86,125)( 87,126)( 88,127)( 89,128)( 90,129)( 91,130)
( 92,144)( 93,145)( 94,146)( 95,147)( 96,148)( 97,149)( 98,150)( 99,151)
(100,152)(101,153)(102,154)(103,155)(104,156)(105,131)(106,132)(107,133)
(108,134)(109,135)(110,136)(111,137)(112,138)(113,139)(114,140)(115,141)
(116,142)(117,143)(157,235)(158,236)(159,237)(160,238)(161,239)(162,240)
(163,241)(164,242)(165,243)(166,244)(167,245)(168,246)(169,247)(170,261)
(171,262)(172,263)(173,264)(174,265)(175,266)(176,267)(177,268)(178,269)
(179,270)(180,271)(181,272)(182,273)(183,248)(184,249)(185,250)(186,251)
(187,252)(188,253)(189,254)(190,255)(191,256)(192,257)(193,258)(194,259)
(195,260)(196,274)(197,275)(198,276)(199,277)(200,278)(201,279)(202,280)
(203,281)(204,282)(205,283)(206,284)(207,285)(208,286)(209,300)(210,301)
(211,302)(212,303)(213,304)(214,305)(215,306)(216,307)(217,308)(218,309)
(219,310)(220,311)(221,312)(222,287)(223,288)(224,289)(225,290)(226,291)
(227,292)(228,293)(229,294)(230,295)(231,296)(232,297)(233,298)(234,299);
s1 := Sym(312)!( 1,170)( 2,182)( 3,181)( 4,180)( 5,179)( 6,178)( 7,177)
( 8,176)( 9,175)( 10,174)( 11,173)( 12,172)( 13,171)( 14,157)( 15,169)
( 16,168)( 17,167)( 18,166)( 19,165)( 20,164)( 21,163)( 22,162)( 23,161)
( 24,160)( 25,159)( 26,158)( 27,183)( 28,195)( 29,194)( 30,193)( 31,192)
( 32,191)( 33,190)( 34,189)( 35,188)( 36,187)( 37,186)( 38,185)( 39,184)
( 40,209)( 41,221)( 42,220)( 43,219)( 44,218)( 45,217)( 46,216)( 47,215)
( 48,214)( 49,213)( 50,212)( 51,211)( 52,210)( 53,196)( 54,208)( 55,207)
( 56,206)( 57,205)( 58,204)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)
( 64,198)( 65,197)( 66,222)( 67,234)( 68,233)( 69,232)( 70,231)( 71,230)
( 72,229)( 73,228)( 74,227)( 75,226)( 76,225)( 77,224)( 78,223)( 79,287)
( 80,299)( 81,298)( 82,297)( 83,296)( 84,295)( 85,294)( 86,293)( 87,292)
( 88,291)( 89,290)( 90,289)( 91,288)( 92,274)( 93,286)( 94,285)( 95,284)
( 96,283)( 97,282)( 98,281)( 99,280)(100,279)(101,278)(102,277)(103,276)
(104,275)(105,300)(106,312)(107,311)(108,310)(109,309)(110,308)(111,307)
(112,306)(113,305)(114,304)(115,303)(116,302)(117,301)(118,248)(119,260)
(120,259)(121,258)(122,257)(123,256)(124,255)(125,254)(126,253)(127,252)
(128,251)(129,250)(130,249)(131,235)(132,247)(133,246)(134,245)(135,244)
(136,243)(137,242)(138,241)(139,240)(140,239)(141,238)(142,237)(143,236)
(144,261)(145,273)(146,272)(147,271)(148,270)(149,269)(150,268)(151,267)
(152,266)(153,265)(154,264)(155,263)(156,262);
s2 := Sym(312)!( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 15)
( 16, 26)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 28)( 29, 39)( 30, 38)
( 31, 37)( 32, 36)( 33, 35)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)
( 46, 48)( 53, 54)( 55, 65)( 56, 64)( 57, 63)( 58, 62)( 59, 61)( 66, 67)
( 68, 78)( 69, 77)( 70, 76)( 71, 75)( 72, 74)( 79, 80)( 81, 91)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)( 92, 93)( 94,104)( 95,103)( 96,102)( 97,101)
( 98,100)(105,106)(107,117)(108,116)(109,115)(110,114)(111,113)(118,119)
(120,130)(121,129)(122,128)(123,127)(124,126)(131,132)(133,143)(134,142)
(135,141)(136,140)(137,139)(144,145)(146,156)(147,155)(148,154)(149,153)
(150,152)(157,158)(159,169)(160,168)(161,167)(162,166)(163,165)(170,171)
(172,182)(173,181)(174,180)(175,179)(176,178)(183,184)(185,195)(186,194)
(187,193)(188,192)(189,191)(196,197)(198,208)(199,207)(200,206)(201,205)
(202,204)(209,210)(211,221)(212,220)(213,219)(214,218)(215,217)(222,223)
(224,234)(225,233)(226,232)(227,231)(228,230)(235,236)(237,247)(238,246)
(239,245)(240,244)(241,243)(248,249)(250,260)(251,259)(252,258)(253,257)
(254,256)(261,262)(263,273)(264,272)(265,271)(266,270)(267,269)(274,275)
(276,286)(277,285)(278,284)(279,283)(280,282)(287,288)(289,299)(290,298)
(291,297)(292,296)(293,295)(300,301)(302,312)(303,311)(304,310)(305,309)
(306,308);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 >;
References : None.
to this polytope