Polytope of Type {26,28}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,28}*1456
Also Known As : {26,28|2}. if this polytope has another name.
Group : SmallGroup(1456,120)
Rank : 3
Schlafli Type : {26,28}
Number of vertices, edges, etc : 26, 364, 28
Order of s0s1s2 : 364
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 : {26,14}*728
7-fold quotients : {26,4}*208
13-fold quotients : {2,28}*112
14-fold quotients : {26,2}*104
26-fold quotients : {2,14}*56
28-fold quotients : {13,2}*52
52-fold quotients : {2,7}*28
91-fold quotients : {2,4}*16
182-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)
(314,325)(315,324)(316,323)(317,322)(318,321)(319,320)(327,338)(328,337)
(329,336)(330,335)(331,334)(332,333)(340,351)(341,350)(342,349)(343,348)
(344,347)(345,346)(353,364)(354,363)(355,362)(356,361)(357,360)(358,359);;
s1 := ( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 80)( 15, 79)
( 16, 91)( 17, 90)( 18, 89)( 19, 88)( 20, 87)( 21, 86)( 22, 85)( 23, 84)
( 24, 83)( 25, 82)( 26, 81)( 27, 67)( 28, 66)( 29, 78)( 30, 77)( 31, 76)
( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 71)( 37, 70)( 38, 69)( 39, 68)
( 40, 54)( 41, 53)( 42, 65)( 43, 64)( 44, 63)( 45, 62)( 46, 61)( 47, 60)
( 48, 59)( 49, 58)( 50, 57)( 51, 56)( 52, 55)( 92, 93)( 94,104)( 95,103)
( 96,102)( 97,101)( 98,100)(105,171)(106,170)(107,182)(108,181)(109,180)
(110,179)(111,178)(112,177)(113,176)(114,175)(115,174)(116,173)(117,172)
(118,158)(119,157)(120,169)(121,168)(122,167)(123,166)(124,165)(125,164)
(126,163)(127,162)(128,161)(129,160)(130,159)(131,145)(132,144)(133,156)
(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)
(142,147)(143,146)(183,275)(184,274)(185,286)(186,285)(187,284)(188,283)
(189,282)(190,281)(191,280)(192,279)(193,278)(194,277)(195,276)(196,353)
(197,352)(198,364)(199,363)(200,362)(201,361)(202,360)(203,359)(204,358)
(205,357)(206,356)(207,355)(208,354)(209,340)(210,339)(211,351)(212,350)
(213,349)(214,348)(215,347)(216,346)(217,345)(218,344)(219,343)(220,342)
(221,341)(222,327)(223,326)(224,338)(225,337)(226,336)(227,335)(228,334)
(229,333)(230,332)(231,331)(232,330)(233,329)(234,328)(235,314)(236,313)
(237,325)(238,324)(239,323)(240,322)(241,321)(242,320)(243,319)(244,318)
(245,317)(246,316)(247,315)(248,301)(249,300)(250,312)(251,311)(252,310)
(253,309)(254,308)(255,307)(256,306)(257,305)(258,304)(259,303)(260,302)
(261,288)(262,287)(263,299)(264,298)(265,297)(266,296)(267,295)(268,294)
(269,293)(270,292)(271,291)(272,290)(273,289);;
s2 := ( 1,196)( 2,197)( 3,198)( 4,199)( 5,200)( 6,201)( 7,202)( 8,203)
( 9,204)( 10,205)( 11,206)( 12,207)( 13,208)( 14,183)( 15,184)( 16,185)
( 17,186)( 18,187)( 19,188)( 20,189)( 21,190)( 22,191)( 23,192)( 24,193)
( 25,194)( 26,195)( 27,261)( 28,262)( 29,263)( 30,264)( 31,265)( 32,266)
( 33,267)( 34,268)( 35,269)( 36,270)( 37,271)( 38,272)( 39,273)( 40,248)
( 41,249)( 42,250)( 43,251)( 44,252)( 45,253)( 46,254)( 47,255)( 48,256)
( 49,257)( 50,258)( 51,259)( 52,260)( 53,235)( 54,236)( 55,237)( 56,238)
( 57,239)( 58,240)( 59,241)( 60,242)( 61,243)( 62,244)( 63,245)( 64,246)
( 65,247)( 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)( 79,209)( 80,210)
( 81,211)( 82,212)( 83,213)( 84,214)( 85,215)( 86,216)( 87,217)( 88,218)
( 89,219)( 90,220)( 91,221)( 92,287)( 93,288)( 94,289)( 95,290)( 96,291)
( 97,292)( 98,293)( 99,294)(100,295)(101,296)(102,297)(103,298)(104,299)
(105,274)(106,275)(107,276)(108,277)(109,278)(110,279)(111,280)(112,281)
(113,282)(114,283)(115,284)(116,285)(117,286)(118,352)(119,353)(120,354)
(121,355)(122,356)(123,357)(124,358)(125,359)(126,360)(127,361)(128,362)
(129,363)(130,364)(131,339)(132,340)(133,341)(134,342)(135,343)(136,344)
(137,345)(138,346)(139,347)(140,348)(141,349)(142,350)(143,351)(144,326)
(145,327)(146,328)(147,329)(148,330)(149,331)(150,332)(151,333)(152,334)
(153,335)(154,336)(155,337)(156,338)(157,313)(158,314)(159,315)(160,316)
(161,317)(162,318)(163,319)(164,320)(165,321)(166,322)(167,323)(168,324)
(169,325)(170,300)(171,301)(172,302)(173,303)(174,304)(175,305)(176,306)
(177,307)(178,308)(179,309)(180,310)(181,311)(182,312);;
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(364)!( 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)(314,325)(315,324)(316,323)(317,322)(318,321)(319,320)(327,338)
(328,337)(329,336)(330,335)(331,334)(332,333)(340,351)(341,350)(342,349)
(343,348)(344,347)(345,346)(353,364)(354,363)(355,362)(356,361)(357,360)
(358,359);
s1 := Sym(364)!( 1, 2)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 14, 80)
( 15, 79)( 16, 91)( 17, 90)( 18, 89)( 19, 88)( 20, 87)( 21, 86)( 22, 85)
( 23, 84)( 24, 83)( 25, 82)( 26, 81)( 27, 67)( 28, 66)( 29, 78)( 30, 77)
( 31, 76)( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 71)( 37, 70)( 38, 69)
( 39, 68)( 40, 54)( 41, 53)( 42, 65)( 43, 64)( 44, 63)( 45, 62)( 46, 61)
( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 51, 56)( 52, 55)( 92, 93)( 94,104)
( 95,103)( 96,102)( 97,101)( 98,100)(105,171)(106,170)(107,182)(108,181)
(109,180)(110,179)(111,178)(112,177)(113,176)(114,175)(115,174)(116,173)
(117,172)(118,158)(119,157)(120,169)(121,168)(122,167)(123,166)(124,165)
(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)(131,145)(132,144)
(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)
(141,148)(142,147)(143,146)(183,275)(184,274)(185,286)(186,285)(187,284)
(188,283)(189,282)(190,281)(191,280)(192,279)(193,278)(194,277)(195,276)
(196,353)(197,352)(198,364)(199,363)(200,362)(201,361)(202,360)(203,359)
(204,358)(205,357)(206,356)(207,355)(208,354)(209,340)(210,339)(211,351)
(212,350)(213,349)(214,348)(215,347)(216,346)(217,345)(218,344)(219,343)
(220,342)(221,341)(222,327)(223,326)(224,338)(225,337)(226,336)(227,335)
(228,334)(229,333)(230,332)(231,331)(232,330)(233,329)(234,328)(235,314)
(236,313)(237,325)(238,324)(239,323)(240,322)(241,321)(242,320)(243,319)
(244,318)(245,317)(246,316)(247,315)(248,301)(249,300)(250,312)(251,311)
(252,310)(253,309)(254,308)(255,307)(256,306)(257,305)(258,304)(259,303)
(260,302)(261,288)(262,287)(263,299)(264,298)(265,297)(266,296)(267,295)
(268,294)(269,293)(270,292)(271,291)(272,290)(273,289);
s2 := Sym(364)!( 1,196)( 2,197)( 3,198)( 4,199)( 5,200)( 6,201)( 7,202)
( 8,203)( 9,204)( 10,205)( 11,206)( 12,207)( 13,208)( 14,183)( 15,184)
( 16,185)( 17,186)( 18,187)( 19,188)( 20,189)( 21,190)( 22,191)( 23,192)
( 24,193)( 25,194)( 26,195)( 27,261)( 28,262)( 29,263)( 30,264)( 31,265)
( 32,266)( 33,267)( 34,268)( 35,269)( 36,270)( 37,271)( 38,272)( 39,273)
( 40,248)( 41,249)( 42,250)( 43,251)( 44,252)( 45,253)( 46,254)( 47,255)
( 48,256)( 49,257)( 50,258)( 51,259)( 52,260)( 53,235)( 54,236)( 55,237)
( 56,238)( 57,239)( 58,240)( 59,241)( 60,242)( 61,243)( 62,244)( 63,245)
( 64,246)( 65,247)( 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)( 79,209)
( 80,210)( 81,211)( 82,212)( 83,213)( 84,214)( 85,215)( 86,216)( 87,217)
( 88,218)( 89,219)( 90,220)( 91,221)( 92,287)( 93,288)( 94,289)( 95,290)
( 96,291)( 97,292)( 98,293)( 99,294)(100,295)(101,296)(102,297)(103,298)
(104,299)(105,274)(106,275)(107,276)(108,277)(109,278)(110,279)(111,280)
(112,281)(113,282)(114,283)(115,284)(116,285)(117,286)(118,352)(119,353)
(120,354)(121,355)(122,356)(123,357)(124,358)(125,359)(126,360)(127,361)
(128,362)(129,363)(130,364)(131,339)(132,340)(133,341)(134,342)(135,343)
(136,344)(137,345)(138,346)(139,347)(140,348)(141,349)(142,350)(143,351)
(144,326)(145,327)(146,328)(147,329)(148,330)(149,331)(150,332)(151,333)
(152,334)(153,335)(154,336)(155,337)(156,338)(157,313)(158,314)(159,315)
(160,316)(161,317)(162,318)(163,319)(164,320)(165,321)(166,322)(167,323)
(168,324)(169,325)(170,300)(171,301)(172,302)(173,303)(174,304)(175,305)
(176,306)(177,307)(178,308)(179,309)(180,310)(181,311)(182,312);
poly := sub<Sym(364)|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*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 >;
References : None.
to this polytope