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Polytope of Type {28,26}

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