Polytope of Type {56,14}

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