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Polytope of Type {14,56}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,56}*1568c
if this polytope has a name.
Group : SmallGroup(1568,530)
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}*784c
   4-fold quotients : {14,14}*392c
   7-fold quotients : {14,8}*224
   8-fold quotients : {7,14}*196
   14-fold quotients : {14,4}*112
   28-fold quotients : {14,2}*56
   49-fold quotients : {2,8}*32
   56-fold quotients : {7,2}*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 := (  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)
(100,105)(101,104)(102,103)(106,141)(107,147)(108,146)(109,145)(110,144)
(111,143)(112,142)(113,134)(114,140)(115,139)(116,138)(117,137)(118,136)
(119,135)(120,127)(121,133)(122,132)(123,131)(124,130)(125,129)(126,128)
(149,154)(150,153)(151,152)(155,190)(156,196)(157,195)(158,194)(159,193)
(160,192)(161,191)(162,183)(163,189)(164,188)(165,187)(166,186)(167,185)
(168,184)(169,176)(170,182)(171,181)(172,180)(173,179)(174,178)(175,177)
(198,203)(199,202)(200,201)(204,239)(205,245)(206,244)(207,243)(208,242)
(209,241)(210,240)(211,232)(212,238)(213,237)(214,236)(215,235)(216,234)
(217,233)(218,225)(219,231)(220,230)(221,229)(222,228)(223,227)(224,226)
(247,252)(248,251)(249,250)(253,288)(254,294)(255,293)(256,292)(257,291)
(258,290)(259,289)(260,281)(261,287)(262,286)(263,285)(264,284)(265,283)
(266,282)(267,274)(268,280)(269,279)(270,278)(271,277)(272,276)(273,275)
(296,301)(297,300)(298,299)(302,337)(303,343)(304,342)(305,341)(306,340)
(307,339)(308,338)(309,330)(310,336)(311,335)(312,334)(313,333)(314,332)
(315,331)(316,323)(317,329)(318,328)(319,327)(320,326)(321,325)(322,324)
(345,350)(346,349)(347,348)(351,386)(352,392)(353,391)(354,390)(355,389)
(356,388)(357,387)(358,379)(359,385)(360,384)(361,383)(362,382)(363,381)
(364,380)(365,372)(366,378)(367,377)(368,376)(369,375)(370,374)(371,373);;
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)( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)
(105,154)(106,190)(107,191)(108,192)(109,193)(110,194)(111,195)(112,196)
(113,183)(114,184)(115,185)(116,186)(117,187)(118,188)(119,189)(120,176)
(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)(127,169)(128,170)
(129,171)(130,172)(131,173)(132,174)(133,175)(134,162)(135,163)(136,164)
(137,165)(138,166)(139,167)(140,168)(141,155)(142,156)(143,157)(144,158)
(145,159)(146,160)(147,161)(197,295)(198,296)(199,297)(200,298)(201,299)
(202,300)(203,301)(204,337)(205,338)(206,339)(207,340)(208,341)(209,342)
(210,343)(211,330)(212,331)(213,332)(214,333)(215,334)(216,335)(217,336)
(218,323)(219,324)(220,325)(221,326)(222,327)(223,328)(224,329)(225,316)
(226,317)(227,318)(228,319)(229,320)(230,321)(231,322)(232,309)(233,310)
(234,311)(235,312)(236,313)(237,314)(238,315)(239,302)(240,303)(241,304)
(242,305)(243,306)(244,307)(245,308)(246,344)(247,345)(248,346)(249,347)
(250,348)(251,349)(252,350)(253,386)(254,387)(255,388)(256,389)(257,390)
(258,391)(259,392)(260,379)(261,380)(262,381)(263,382)(264,383)(265,384)
(266,385)(267,372)(268,373)(269,374)(270,375)(271,376)(272,377)(273,378)
(274,365)(275,366)(276,367)(277,368)(278,369)(279,370)(280,371)(281,358)
(282,359)(283,360)(284,361)(285,362)(286,363)(287,364)(288,351)(289,352)
(290,353)(291,354)(292,355)(293,356)(294,357);;
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*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*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 ];;
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)(100,105)(101,104)(102,103)(106,141)(107,147)(108,146)(109,145)
(110,144)(111,143)(112,142)(113,134)(114,140)(115,139)(116,138)(117,137)
(118,136)(119,135)(120,127)(121,133)(122,132)(123,131)(124,130)(125,129)
(126,128)(149,154)(150,153)(151,152)(155,190)(156,196)(157,195)(158,194)
(159,193)(160,192)(161,191)(162,183)(163,189)(164,188)(165,187)(166,186)
(167,185)(168,184)(169,176)(170,182)(171,181)(172,180)(173,179)(174,178)
(175,177)(198,203)(199,202)(200,201)(204,239)(205,245)(206,244)(207,243)
(208,242)(209,241)(210,240)(211,232)(212,238)(213,237)(214,236)(215,235)
(216,234)(217,233)(218,225)(219,231)(220,230)(221,229)(222,228)(223,227)
(224,226)(247,252)(248,251)(249,250)(253,288)(254,294)(255,293)(256,292)
(257,291)(258,290)(259,289)(260,281)(261,287)(262,286)(263,285)(264,284)
(265,283)(266,282)(267,274)(268,280)(269,279)(270,278)(271,277)(272,276)
(273,275)(296,301)(297,300)(298,299)(302,337)(303,343)(304,342)(305,341)
(306,340)(307,339)(308,338)(309,330)(310,336)(311,335)(312,334)(313,333)
(314,332)(315,331)(316,323)(317,329)(318,328)(319,327)(320,326)(321,325)
(322,324)(345,350)(346,349)(347,348)(351,386)(352,392)(353,391)(354,390)
(355,389)(356,388)(357,387)(358,379)(359,385)(360,384)(361,383)(362,382)
(363,381)(364,380)(365,372)(366,378)(367,377)(368,376)(369,375)(370,374)
(371,373);
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)( 99,148)(100,149)(101,150)(102,151)(103,152)
(104,153)(105,154)(106,190)(107,191)(108,192)(109,193)(110,194)(111,195)
(112,196)(113,183)(114,184)(115,185)(116,186)(117,187)(118,188)(119,189)
(120,176)(121,177)(122,178)(123,179)(124,180)(125,181)(126,182)(127,169)
(128,170)(129,171)(130,172)(131,173)(132,174)(133,175)(134,162)(135,163)
(136,164)(137,165)(138,166)(139,167)(140,168)(141,155)(142,156)(143,157)
(144,158)(145,159)(146,160)(147,161)(197,295)(198,296)(199,297)(200,298)
(201,299)(202,300)(203,301)(204,337)(205,338)(206,339)(207,340)(208,341)
(209,342)(210,343)(211,330)(212,331)(213,332)(214,333)(215,334)(216,335)
(217,336)(218,323)(219,324)(220,325)(221,326)(222,327)(223,328)(224,329)
(225,316)(226,317)(227,318)(228,319)(229,320)(230,321)(231,322)(232,309)
(233,310)(234,311)(235,312)(236,313)(237,314)(238,315)(239,302)(240,303)
(241,304)(242,305)(243,306)(244,307)(245,308)(246,344)(247,345)(248,346)
(249,347)(250,348)(251,349)(252,350)(253,386)(254,387)(255,388)(256,389)
(257,390)(258,391)(259,392)(260,379)(261,380)(262,381)(263,382)(264,383)
(265,384)(266,385)(267,372)(268,373)(269,374)(270,375)(271,376)(272,377)
(273,378)(274,365)(275,366)(276,367)(277,368)(278,369)(279,370)(280,371)
(281,358)(282,359)(283,360)(284,361)(285,362)(286,363)(287,364)(288,351)
(289,352)(290,353)(291,354)(292,355)(293,356)(294,357);
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*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*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 >; 
 
References : None.
to this polytope