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Polytope of Type {56,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,14}*1568b
if this polytope has a name.
Group : SmallGroup(1568,397)
Rank : 3
Schlafli Type : {56,14}
Number of vertices, edges, etc : 56, 392, 14
Order of s0s1s2 : 56
Order of s0s1s2s1 : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {28,14}*784b
   4-fold quotients : {14,14}*392c
   7-fold quotients : {56,2}*224
   8-fold quotients : {7,14}*196
   14-fold quotients : {28,2}*112
   28-fold quotients : {14,2}*56
   49-fold quotients : {8,2}*32
   56-fold quotients : {7,2}*28
   98-fold quotients : {4,2}*16
   196-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  7)(  3,  6)(  4,  5)(  8, 43)(  9, 49)( 10, 48)( 11, 47)( 12, 46)
( 13, 45)( 14, 44)( 15, 36)( 16, 42)( 17, 41)( 18, 40)( 19, 39)( 20, 38)
( 21, 37)( 22, 29)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 51, 56)( 52, 55)( 53, 54)( 57, 92)( 58, 98)( 59, 97)( 60, 96)( 61, 95)
( 62, 94)( 63, 93)( 64, 85)( 65, 91)( 66, 90)( 67, 89)( 68, 88)( 69, 87)
( 70, 86)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(106,190)
(107,196)(108,195)(109,194)(110,193)(111,192)(112,191)(113,183)(114,189)
(115,188)(116,187)(117,186)(118,185)(119,184)(120,176)(121,182)(122,181)
(123,180)(124,179)(125,178)(126,177)(127,169)(128,175)(129,174)(130,173)
(131,172)(132,171)(133,170)(134,162)(135,168)(136,167)(137,166)(138,165)
(139,164)(140,163)(141,155)(142,161)(143,160)(144,159)(145,158)(146,157)
(147,156)(197,295)(198,301)(199,300)(200,299)(201,298)(202,297)(203,296)
(204,337)(205,343)(206,342)(207,341)(208,340)(209,339)(210,338)(211,330)
(212,336)(213,335)(214,334)(215,333)(216,332)(217,331)(218,323)(219,329)
(220,328)(221,327)(222,326)(223,325)(224,324)(225,316)(226,322)(227,321)
(228,320)(229,319)(230,318)(231,317)(232,309)(233,315)(234,314)(235,313)
(236,312)(237,311)(238,310)(239,302)(240,308)(241,307)(242,306)(243,305)
(244,304)(245,303)(246,344)(247,350)(248,349)(249,348)(250,347)(251,346)
(252,345)(253,386)(254,392)(255,391)(256,390)(257,389)(258,388)(259,387)
(260,379)(261,385)(262,384)(263,383)(264,382)(265,381)(266,380)(267,372)
(268,378)(269,377)(270,376)(271,375)(272,374)(273,373)(274,365)(275,371)
(276,370)(277,369)(278,368)(279,367)(280,366)(281,358)(282,364)(283,363)
(284,362)(285,361)(286,360)(287,359)(288,351)(289,357)(290,356)(291,355)
(292,354)(293,353)(294,352);;
s1 := (  1,205)(  2,204)(  3,210)(  4,209)(  5,208)(  6,207)(  7,206)(  8,198)
(  9,197)( 10,203)( 11,202)( 12,201)( 13,200)( 14,199)( 15,240)( 16,239)
( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,233)( 23,232)( 24,238)
( 25,237)( 26,236)( 27,235)( 28,234)( 29,226)( 30,225)( 31,231)( 32,230)
( 33,229)( 34,228)( 35,227)( 36,219)( 37,218)( 38,224)( 39,223)( 40,222)
( 41,221)( 42,220)( 43,212)( 44,211)( 45,217)( 46,216)( 47,215)( 48,214)
( 49,213)( 50,254)( 51,253)( 52,259)( 53,258)( 54,257)( 55,256)( 56,255)
( 57,247)( 58,246)( 59,252)( 60,251)( 61,250)( 62,249)( 63,248)( 64,289)
( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 71,282)( 72,281)
( 73,287)( 74,286)( 75,285)( 76,284)( 77,283)( 78,275)( 79,274)( 80,280)
( 81,279)( 82,278)( 83,277)( 84,276)( 85,268)( 86,267)( 87,273)( 88,272)
( 89,271)( 90,270)( 91,269)( 92,261)( 93,260)( 94,266)( 95,265)( 96,264)
( 97,263)( 98,262)( 99,352)(100,351)(101,357)(102,356)(103,355)(104,354)
(105,353)(106,345)(107,344)(108,350)(109,349)(110,348)(111,347)(112,346)
(113,387)(114,386)(115,392)(116,391)(117,390)(118,389)(119,388)(120,380)
(121,379)(122,385)(123,384)(124,383)(125,382)(126,381)(127,373)(128,372)
(129,378)(130,377)(131,376)(132,375)(133,374)(134,366)(135,365)(136,371)
(137,370)(138,369)(139,368)(140,367)(141,359)(142,358)(143,364)(144,363)
(145,362)(146,361)(147,360)(148,303)(149,302)(150,308)(151,307)(152,306)
(153,305)(154,304)(155,296)(156,295)(157,301)(158,300)(159,299)(160,298)
(161,297)(162,338)(163,337)(164,343)(165,342)(166,341)(167,340)(168,339)
(169,331)(170,330)(171,336)(172,335)(173,334)(174,333)(175,332)(176,324)
(177,323)(178,329)(179,328)(180,327)(181,326)(182,325)(183,317)(184,316)
(185,322)(186,321)(187,320)(188,319)(189,318)(190,310)(191,309)(192,315)
(193,314)(194,313)(195,312)(196,311);;
s2 := (  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 36)
( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)( 23, 30)
( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 57, 92)( 58, 93)( 59, 94)
( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)( 67, 88)
( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)
( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)(111,146)
(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)
(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)(155,190)
(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)
(164,185)(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)(171,178)
(172,179)(173,180)(174,181)(175,182)(204,239)(205,240)(206,241)(207,242)
(208,243)(209,244)(210,245)(211,232)(212,233)(213,234)(214,235)(215,236)
(216,237)(217,238)(218,225)(219,226)(220,227)(221,228)(222,229)(223,230)
(224,231)(253,288)(254,289)(255,290)(256,291)(257,292)(258,293)(259,294)
(260,281)(261,282)(262,283)(263,284)(264,285)(265,286)(266,287)(267,274)
(268,275)(269,276)(270,277)(271,278)(272,279)(273,280)(302,337)(303,338)
(304,339)(305,340)(306,341)(307,342)(308,343)(309,330)(310,331)(311,332)
(312,333)(313,334)(314,335)(315,336)(316,323)(317,324)(318,325)(319,326)
(320,327)(321,328)(322,329)(351,386)(352,387)(353,388)(354,389)(355,390)
(356,391)(357,392)(358,379)(359,380)(360,381)(361,382)(362,383)(363,384)
(364,385)(365,372)(366,373)(367,374)(368,375)(369,376)(370,377)(371,378);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(392)!(  2,  7)(  3,  6)(  4,  5)(  8, 43)(  9, 49)( 10, 48)( 11, 47)
( 12, 46)( 13, 45)( 14, 44)( 15, 36)( 16, 42)( 17, 41)( 18, 40)( 19, 39)
( 20, 38)( 21, 37)( 22, 29)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)
( 28, 30)( 51, 56)( 52, 55)( 53, 54)( 57, 92)( 58, 98)( 59, 97)( 60, 96)
( 61, 95)( 62, 94)( 63, 93)( 64, 85)( 65, 91)( 66, 90)( 67, 89)( 68, 88)
( 69, 87)( 70, 86)( 71, 78)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)
( 77, 79)( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)
(106,190)(107,196)(108,195)(109,194)(110,193)(111,192)(112,191)(113,183)
(114,189)(115,188)(116,187)(117,186)(118,185)(119,184)(120,176)(121,182)
(122,181)(123,180)(124,179)(125,178)(126,177)(127,169)(128,175)(129,174)
(130,173)(131,172)(132,171)(133,170)(134,162)(135,168)(136,167)(137,166)
(138,165)(139,164)(140,163)(141,155)(142,161)(143,160)(144,159)(145,158)
(146,157)(147,156)(197,295)(198,301)(199,300)(200,299)(201,298)(202,297)
(203,296)(204,337)(205,343)(206,342)(207,341)(208,340)(209,339)(210,338)
(211,330)(212,336)(213,335)(214,334)(215,333)(216,332)(217,331)(218,323)
(219,329)(220,328)(221,327)(222,326)(223,325)(224,324)(225,316)(226,322)
(227,321)(228,320)(229,319)(230,318)(231,317)(232,309)(233,315)(234,314)
(235,313)(236,312)(237,311)(238,310)(239,302)(240,308)(241,307)(242,306)
(243,305)(244,304)(245,303)(246,344)(247,350)(248,349)(249,348)(250,347)
(251,346)(252,345)(253,386)(254,392)(255,391)(256,390)(257,389)(258,388)
(259,387)(260,379)(261,385)(262,384)(263,383)(264,382)(265,381)(266,380)
(267,372)(268,378)(269,377)(270,376)(271,375)(272,374)(273,373)(274,365)
(275,371)(276,370)(277,369)(278,368)(279,367)(280,366)(281,358)(282,364)
(283,363)(284,362)(285,361)(286,360)(287,359)(288,351)(289,357)(290,356)
(291,355)(292,354)(293,353)(294,352);
s1 := Sym(392)!(  1,205)(  2,204)(  3,210)(  4,209)(  5,208)(  6,207)(  7,206)
(  8,198)(  9,197)( 10,203)( 11,202)( 12,201)( 13,200)( 14,199)( 15,240)
( 16,239)( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,233)( 23,232)
( 24,238)( 25,237)( 26,236)( 27,235)( 28,234)( 29,226)( 30,225)( 31,231)
( 32,230)( 33,229)( 34,228)( 35,227)( 36,219)( 37,218)( 38,224)( 39,223)
( 40,222)( 41,221)( 42,220)( 43,212)( 44,211)( 45,217)( 46,216)( 47,215)
( 48,214)( 49,213)( 50,254)( 51,253)( 52,259)( 53,258)( 54,257)( 55,256)
( 56,255)( 57,247)( 58,246)( 59,252)( 60,251)( 61,250)( 62,249)( 63,248)
( 64,289)( 65,288)( 66,294)( 67,293)( 68,292)( 69,291)( 70,290)( 71,282)
( 72,281)( 73,287)( 74,286)( 75,285)( 76,284)( 77,283)( 78,275)( 79,274)
( 80,280)( 81,279)( 82,278)( 83,277)( 84,276)( 85,268)( 86,267)( 87,273)
( 88,272)( 89,271)( 90,270)( 91,269)( 92,261)( 93,260)( 94,266)( 95,265)
( 96,264)( 97,263)( 98,262)( 99,352)(100,351)(101,357)(102,356)(103,355)
(104,354)(105,353)(106,345)(107,344)(108,350)(109,349)(110,348)(111,347)
(112,346)(113,387)(114,386)(115,392)(116,391)(117,390)(118,389)(119,388)
(120,380)(121,379)(122,385)(123,384)(124,383)(125,382)(126,381)(127,373)
(128,372)(129,378)(130,377)(131,376)(132,375)(133,374)(134,366)(135,365)
(136,371)(137,370)(138,369)(139,368)(140,367)(141,359)(142,358)(143,364)
(144,363)(145,362)(146,361)(147,360)(148,303)(149,302)(150,308)(151,307)
(152,306)(153,305)(154,304)(155,296)(156,295)(157,301)(158,300)(159,299)
(160,298)(161,297)(162,338)(163,337)(164,343)(165,342)(166,341)(167,340)
(168,339)(169,331)(170,330)(171,336)(172,335)(173,334)(174,333)(175,332)
(176,324)(177,323)(178,329)(179,328)(180,327)(181,326)(182,325)(183,317)
(184,316)(185,322)(186,321)(187,320)(188,319)(189,318)(190,310)(191,309)
(192,315)(193,314)(194,313)(195,312)(196,311);
s2 := Sym(392)!(  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)
( 15, 36)( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)
( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 57, 92)( 58, 93)
( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)
( 67, 88)( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)
( 75, 82)( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)
(111,146)(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)
(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)
(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)
(163,184)(164,185)(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)
(171,178)(172,179)(173,180)(174,181)(175,182)(204,239)(205,240)(206,241)
(207,242)(208,243)(209,244)(210,245)(211,232)(212,233)(213,234)(214,235)
(215,236)(216,237)(217,238)(218,225)(219,226)(220,227)(221,228)(222,229)
(223,230)(224,231)(253,288)(254,289)(255,290)(256,291)(257,292)(258,293)
(259,294)(260,281)(261,282)(262,283)(263,284)(264,285)(265,286)(266,287)
(267,274)(268,275)(269,276)(270,277)(271,278)(272,279)(273,280)(302,337)
(303,338)(304,339)(305,340)(306,341)(307,342)(308,343)(309,330)(310,331)
(311,332)(312,333)(313,334)(314,335)(315,336)(316,323)(317,324)(318,325)
(319,326)(320,327)(321,328)(322,329)(351,386)(352,387)(353,388)(354,389)
(355,390)(356,391)(357,392)(358,379)(359,380)(360,381)(361,382)(362,383)
(363,384)(364,385)(365,372)(366,373)(367,374)(368,375)(369,376)(370,377)
(371,378);
poly := sub<Sym(392)|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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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