Polytope of Type {14,56}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,56}*1568b
if this polytope has a name.
Group : SmallGroup(1568,397)
Rank : 3
Schlafli Type : {14,56}
Number of vertices, edges, etc : 14, 392, 56
Order of s₀s₁s₂ : 56
Order of s₀s₁s₂s₁ : 14
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 : {14,28}*784b
   4-fold quotients : {14,14}*392b
   7-fold quotients : {2,56}*224
   8-fold quotients : {14,7}*196
   14-fold quotients : {2,28}*112
   28-fold quotients : {2,14}*56
   49-fold quotients : {2,8}*32
   56-fold quotients : {2,7}*28
   98-fold quotients : {2,4}*16
   196-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  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);;
s1 := (  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 15, 43)
( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)( 23, 42)
( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)( 32, 33)
( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 64, 92)
( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)( 72, 91)
( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)( 81, 82)
( 99,155)(100,161)(101,160)(102,159)(103,158)(104,157)(105,156)(106,148)
(107,154)(108,153)(109,152)(110,151)(111,150)(112,149)(113,190)(114,196)
(115,195)(116,194)(117,193)(118,192)(119,191)(120,183)(121,189)(122,188)
(123,187)(124,186)(125,185)(126,184)(127,176)(128,182)(129,181)(130,180)
(131,179)(132,178)(133,177)(134,169)(135,175)(136,174)(137,173)(138,172)
(139,171)(140,170)(141,162)(142,168)(143,167)(144,166)(145,165)(146,164)
(147,163)(197,302)(198,308)(199,307)(200,306)(201,305)(202,304)(203,303)
(204,295)(205,301)(206,300)(207,299)(208,298)(209,297)(210,296)(211,337)
(212,343)(213,342)(214,341)(215,340)(216,339)(217,338)(218,330)(219,336)
(220,335)(221,334)(222,333)(223,332)(224,331)(225,323)(226,329)(227,328)
(228,327)(229,326)(230,325)(231,324)(232,316)(233,322)(234,321)(235,320)
(236,319)(237,318)(238,317)(239,309)(240,315)(241,314)(242,313)(243,312)
(244,311)(245,310)(246,351)(247,357)(248,356)(249,355)(250,354)(251,353)
(252,352)(253,344)(254,350)(255,349)(256,348)(257,347)(258,346)(259,345)
(260,386)(261,392)(262,391)(263,390)(264,389)(265,388)(266,387)(267,379)
(268,385)(269,384)(270,383)(271,382)(272,381)(273,380)(274,372)(275,378)
(276,377)(277,376)(278,375)(279,374)(280,373)(281,365)(282,371)(283,370)
(284,369)(285,368)(286,367)(287,366)(288,358)(289,364)(290,363)(291,362)
(292,361)(293,360)(294,359);;
s2 := (  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);;
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*s0*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, 
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*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(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);
s1 := Sym(392)!(  1,  8)(  2, 14)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)
( 15, 43)( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)
( 23, 42)( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)
( 32, 33)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)
( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)
( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)
( 81, 82)( 99,155)(100,161)(101,160)(102,159)(103,158)(104,157)(105,156)
(106,148)(107,154)(108,153)(109,152)(110,151)(111,150)(112,149)(113,190)
(114,196)(115,195)(116,194)(117,193)(118,192)(119,191)(120,183)(121,189)
(122,188)(123,187)(124,186)(125,185)(126,184)(127,176)(128,182)(129,181)
(130,180)(131,179)(132,178)(133,177)(134,169)(135,175)(136,174)(137,173)
(138,172)(139,171)(140,170)(141,162)(142,168)(143,167)(144,166)(145,165)
(146,164)(147,163)(197,302)(198,308)(199,307)(200,306)(201,305)(202,304)
(203,303)(204,295)(205,301)(206,300)(207,299)(208,298)(209,297)(210,296)
(211,337)(212,343)(213,342)(214,341)(215,340)(216,339)(217,338)(218,330)
(219,336)(220,335)(221,334)(222,333)(223,332)(224,331)(225,323)(226,329)
(227,328)(228,327)(229,326)(230,325)(231,324)(232,316)(233,322)(234,321)
(235,320)(236,319)(237,318)(238,317)(239,309)(240,315)(241,314)(242,313)
(243,312)(244,311)(245,310)(246,351)(247,357)(248,356)(249,355)(250,354)
(251,353)(252,352)(253,344)(254,350)(255,349)(256,348)(257,347)(258,346)
(259,345)(260,386)(261,392)(262,391)(263,390)(264,389)(265,388)(266,387)
(267,379)(268,385)(269,384)(270,383)(271,382)(272,381)(273,380)(274,372)
(275,378)(276,377)(277,376)(278,375)(279,374)(280,373)(281,365)(282,371)
(283,370)(284,369)(285,368)(286,367)(287,366)(288,358)(289,364)(290,363)
(291,362)(292,361)(293,360)(294,359);
s2 := 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);
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*s0*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, 
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*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