Polytope of Type {56,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {56,14}*1568c
if this polytope has a name.
Group : SmallGroup(1568,530)
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
   Self-Petrie
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}*784c
   4-fold quotients : {14,14}*392b
   7-fold quotients : {8,14}*224
   8-fold quotients : {14,7}*196
   14-fold quotients : {4,14}*112
   28-fold quotients : {2,14}*56
   49-fold quotients : {8,2}*32
   56-fold quotients : {2,7}*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 := (  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);;
s1 := (  1,204)(  2,210)(  3,209)(  4,208)(  5,207)(  6,206)(  7,205)(  8,197)
(  9,203)( 10,202)( 11,201)( 12,200)( 13,199)( 14,198)( 15,239)( 16,245)
( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,232)( 23,238)( 24,237)
( 25,236)( 26,235)( 27,234)( 28,233)( 29,225)( 30,231)( 31,230)( 32,229)
( 33,228)( 34,227)( 35,226)( 36,218)( 37,224)( 38,223)( 39,222)( 40,221)
( 41,220)( 42,219)( 43,211)( 44,217)( 45,216)( 46,215)( 47,214)( 48,213)
( 49,212)( 50,253)( 51,259)( 52,258)( 53,257)( 54,256)( 55,255)( 56,254)
( 57,246)( 58,252)( 59,251)( 60,250)( 61,249)( 62,248)( 63,247)( 64,288)
( 65,294)( 66,293)( 67,292)( 68,291)( 69,290)( 70,289)( 71,281)( 72,287)
( 73,286)( 74,285)( 75,284)( 76,283)( 77,282)( 78,274)( 79,280)( 80,279)
( 81,278)( 82,277)( 83,276)( 84,275)( 85,267)( 86,273)( 87,272)( 88,271)
( 89,270)( 90,269)( 91,268)( 92,260)( 93,266)( 94,265)( 95,264)( 96,263)
( 97,262)( 98,261)( 99,351)(100,357)(101,356)(102,355)(103,354)(104,353)
(105,352)(106,344)(107,350)(108,349)(109,348)(110,347)(111,346)(112,345)
(113,386)(114,392)(115,391)(116,390)(117,389)(118,388)(119,387)(120,379)
(121,385)(122,384)(123,383)(124,382)(125,381)(126,380)(127,372)(128,378)
(129,377)(130,376)(131,375)(132,374)(133,373)(134,365)(135,371)(136,370)
(137,369)(138,368)(139,367)(140,366)(141,358)(142,364)(143,363)(144,362)
(145,361)(146,360)(147,359)(148,302)(149,308)(150,307)(151,306)(152,305)
(153,304)(154,303)(155,295)(156,301)(157,300)(158,299)(159,298)(160,297)
(161,296)(162,337)(163,343)(164,342)(165,341)(166,340)(167,339)(168,338)
(169,330)(170,336)(171,335)(172,334)(173,333)(174,332)(175,331)(176,323)
(177,329)(178,328)(179,327)(180,326)(181,325)(182,324)(183,316)(184,322)
(185,321)(186,320)(187,319)(188,318)(189,317)(190,309)(191,315)(192,314)
(193,313)(194,312)(195,311)(196,310);;
s2 := (  1,  2)(  3,  7)(  4,  6)(  8, 44)(  9, 43)( 10, 49)( 11, 48)( 12, 47)
( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)( 20, 39)
( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)
( 50, 51)( 52, 56)( 53, 55)( 57, 93)( 58, 92)( 59, 98)( 60, 97)( 61, 96)
( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)( 69, 88)
( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)
( 99,100)(101,105)(102,104)(106,142)(107,141)(108,147)(109,146)(110,145)
(111,144)(112,143)(113,135)(114,134)(115,140)(116,139)(117,138)(118,137)
(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)(126,129)
(148,149)(150,154)(151,153)(155,191)(156,190)(157,196)(158,195)(159,194)
(160,193)(161,192)(162,184)(163,183)(164,189)(165,188)(166,187)(167,186)
(168,185)(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)(175,178)
(197,198)(199,203)(200,202)(204,240)(205,239)(206,245)(207,244)(208,243)
(209,242)(210,241)(211,233)(212,232)(213,238)(214,237)(215,236)(216,235)
(217,234)(218,226)(219,225)(220,231)(221,230)(222,229)(223,228)(224,227)
(246,247)(248,252)(249,251)(253,289)(254,288)(255,294)(256,293)(257,292)
(258,291)(259,290)(260,282)(261,281)(262,287)(263,286)(264,285)(265,284)
(266,283)(267,275)(268,274)(269,280)(270,279)(271,278)(272,277)(273,276)
(295,296)(297,301)(298,300)(302,338)(303,337)(304,343)(305,342)(306,341)
(307,340)(308,339)(309,331)(310,330)(311,336)(312,335)(313,334)(314,333)
(315,332)(316,324)(317,323)(318,329)(319,328)(320,327)(321,326)(322,325)
(344,345)(346,350)(347,349)(351,387)(352,386)(353,392)(354,391)(355,390)
(356,389)(357,388)(358,380)(359,379)(360,385)(361,384)(362,383)(363,382)
(364,381)(365,373)(366,372)(367,378)(368,377)(369,376)(370,375)(371,374);;
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*s0*s1*s0*s1*s0*s1*s2*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 ];;
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)( 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);
s1 := Sym(392)!(  1,204)(  2,210)(  3,209)(  4,208)(  5,207)(  6,206)(  7,205)
(  8,197)(  9,203)( 10,202)( 11,201)( 12,200)( 13,199)( 14,198)( 15,239)
( 16,245)( 17,244)( 18,243)( 19,242)( 20,241)( 21,240)( 22,232)( 23,238)
( 24,237)( 25,236)( 26,235)( 27,234)( 28,233)( 29,225)( 30,231)( 31,230)
( 32,229)( 33,228)( 34,227)( 35,226)( 36,218)( 37,224)( 38,223)( 39,222)
( 40,221)( 41,220)( 42,219)( 43,211)( 44,217)( 45,216)( 46,215)( 47,214)
( 48,213)( 49,212)( 50,253)( 51,259)( 52,258)( 53,257)( 54,256)( 55,255)
( 56,254)( 57,246)( 58,252)( 59,251)( 60,250)( 61,249)( 62,248)( 63,247)
( 64,288)( 65,294)( 66,293)( 67,292)( 68,291)( 69,290)( 70,289)( 71,281)
( 72,287)( 73,286)( 74,285)( 75,284)( 76,283)( 77,282)( 78,274)( 79,280)
( 80,279)( 81,278)( 82,277)( 83,276)( 84,275)( 85,267)( 86,273)( 87,272)
( 88,271)( 89,270)( 90,269)( 91,268)( 92,260)( 93,266)( 94,265)( 95,264)
( 96,263)( 97,262)( 98,261)( 99,351)(100,357)(101,356)(102,355)(103,354)
(104,353)(105,352)(106,344)(107,350)(108,349)(109,348)(110,347)(111,346)
(112,345)(113,386)(114,392)(115,391)(116,390)(117,389)(118,388)(119,387)
(120,379)(121,385)(122,384)(123,383)(124,382)(125,381)(126,380)(127,372)
(128,378)(129,377)(130,376)(131,375)(132,374)(133,373)(134,365)(135,371)
(136,370)(137,369)(138,368)(139,367)(140,366)(141,358)(142,364)(143,363)
(144,362)(145,361)(146,360)(147,359)(148,302)(149,308)(150,307)(151,306)
(152,305)(153,304)(154,303)(155,295)(156,301)(157,300)(158,299)(159,298)
(160,297)(161,296)(162,337)(163,343)(164,342)(165,341)(166,340)(167,339)
(168,338)(169,330)(170,336)(171,335)(172,334)(173,333)(174,332)(175,331)
(176,323)(177,329)(178,328)(179,327)(180,326)(181,325)(182,324)(183,316)
(184,322)(185,321)(186,320)(187,319)(188,318)(189,317)(190,309)(191,315)
(192,314)(193,313)(194,312)(195,311)(196,310);
s2 := Sym(392)!(  1,  2)(  3,  7)(  4,  6)(  8, 44)(  9, 43)( 10, 49)( 11, 48)
( 12, 47)( 13, 46)( 14, 45)( 15, 37)( 16, 36)( 17, 42)( 18, 41)( 19, 40)
( 20, 39)( 21, 38)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)
( 28, 31)( 50, 51)( 52, 56)( 53, 55)( 57, 93)( 58, 92)( 59, 98)( 60, 97)
( 61, 96)( 62, 95)( 63, 94)( 64, 86)( 65, 85)( 66, 91)( 67, 90)( 68, 89)
( 69, 88)( 70, 87)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)
( 77, 80)( 99,100)(101,105)(102,104)(106,142)(107,141)(108,147)(109,146)
(110,145)(111,144)(112,143)(113,135)(114,134)(115,140)(116,139)(117,138)
(118,137)(119,136)(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)
(126,129)(148,149)(150,154)(151,153)(155,191)(156,190)(157,196)(158,195)
(159,194)(160,193)(161,192)(162,184)(163,183)(164,189)(165,188)(166,187)
(167,186)(168,185)(169,177)(170,176)(171,182)(172,181)(173,180)(174,179)
(175,178)(197,198)(199,203)(200,202)(204,240)(205,239)(206,245)(207,244)
(208,243)(209,242)(210,241)(211,233)(212,232)(213,238)(214,237)(215,236)
(216,235)(217,234)(218,226)(219,225)(220,231)(221,230)(222,229)(223,228)
(224,227)(246,247)(248,252)(249,251)(253,289)(254,288)(255,294)(256,293)
(257,292)(258,291)(259,290)(260,282)(261,281)(262,287)(263,286)(264,285)
(265,284)(266,283)(267,275)(268,274)(269,280)(270,279)(271,278)(272,277)
(273,276)(295,296)(297,301)(298,300)(302,338)(303,337)(304,343)(305,342)
(306,341)(307,340)(308,339)(309,331)(310,330)(311,336)(312,335)(313,334)
(314,333)(315,332)(316,324)(317,323)(318,329)(319,328)(320,327)(321,326)
(322,325)(344,345)(346,350)(347,349)(351,387)(352,386)(353,392)(354,391)
(355,390)(356,389)(357,388)(358,380)(359,379)(360,385)(361,384)(362,383)
(363,382)(364,381)(365,373)(366,372)(367,378)(368,377)(369,376)(370,375)
(371,374);
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*s0*s1*s0*s1*s0*s1*s2*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 >;

References : None.
to this polytope