Polytope of Type {28,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {28,28}*1568c
if this polytope has a name.
Group : SmallGroup(1568,527)
Rank : 3
Schlafli Type : {28,28}
Number of vertices, edges, etc : 28, 392, 28
Order of s₀s₁s₂ : 28
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, {14,28}*784c
   4-fold quotients : {14,14}*392c
   7-fold quotients : {28,4}*224
   8-fold quotients : {7,14}*196
   14-fold quotients : {28,2}*112, {14,4}*112
   28-fold quotients : {14,2}*56
   49-fold quotients : {4,4}*32
   56-fold quotients : {7,2}*28
   98-fold quotients : {2,4}*16, {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)
(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)
(197,344)(198,350)(199,349)(200,348)(201,347)(202,346)(203,345)(204,386)
(205,392)(206,391)(207,390)(208,389)(209,388)(210,387)(211,379)(212,385)
(213,384)(214,383)(215,382)(216,381)(217,380)(218,372)(219,378)(220,377)
(221,376)(222,375)(223,374)(224,373)(225,365)(226,371)(227,370)(228,369)
(229,368)(230,367)(231,366)(232,358)(233,364)(234,363)(235,362)(236,361)
(237,360)(238,359)(239,351)(240,357)(241,356)(242,355)(243,354)(244,353)
(245,352)(246,295)(247,301)(248,300)(249,299)(250,298)(251,297)(252,296)
(253,337)(254,343)(255,342)(256,341)(257,340)(258,339)(259,338)(260,330)
(261,336)(262,335)(263,334)(264,333)(265,332)(266,331)(267,323)(268,329)
(269,328)(270,327)(271,326)(272,325)(273,324)(274,316)(275,322)(276,321)
(277,320)(278,319)(279,318)(280,317)(281,309)(282,315)(283,314)(284,313)
(285,312)(286,311)(287,310)(288,302)(289,308)(290,307)(291,306)(292,305)
(293,304)(294,303);;
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)( 99,303)(100,302)(101,308)(102,307)(103,306)(104,305)
(105,304)(106,296)(107,295)(108,301)(109,300)(110,299)(111,298)(112,297)
(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)(120,331)
(121,330)(122,336)(123,335)(124,334)(125,333)(126,332)(127,324)(128,323)
(129,329)(130,328)(131,327)(132,326)(133,325)(134,317)(135,316)(136,322)
(137,321)(138,320)(139,319)(140,318)(141,310)(142,309)(143,315)(144,314)
(145,313)(146,312)(147,311)(148,352)(149,351)(150,357)(151,356)(152,355)
(153,354)(154,353)(155,345)(156,344)(157,350)(158,349)(159,348)(160,347)
(161,346)(162,387)(163,386)(164,392)(165,391)(166,390)(167,389)(168,388)
(169,380)(170,379)(171,385)(172,384)(173,383)(174,382)(175,381)(176,373)
(177,372)(178,378)(179,377)(180,376)(181,375)(182,374)(183,366)(184,365)
(185,371)(186,370)(187,369)(188,368)(189,367)(190,359)(191,358)(192,364)
(193,363)(194,362)(195,361)(196,360);;
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)(197,246)(198,247)(199,248)(200,249)
(201,250)(202,251)(203,252)(204,288)(205,289)(206,290)(207,291)(208,292)
(209,293)(210,294)(211,281)(212,282)(213,283)(214,284)(215,285)(216,286)
(217,287)(218,274)(219,275)(220,276)(221,277)(222,278)(223,279)(224,280)
(225,267)(226,268)(227,269)(228,270)(229,271)(230,272)(231,273)(232,260)
(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,253)(240,254)
(241,255)(242,256)(243,257)(244,258)(245,259)(295,344)(296,345)(297,346)
(298,347)(299,348)(300,349)(301,350)(302,386)(303,387)(304,388)(305,389)
(306,390)(307,391)(308,392)(309,379)(310,380)(311,381)(312,382)(313,383)
(314,384)(315,385)(316,372)(317,373)(318,374)(319,375)(320,376)(321,377)
(322,378)(323,365)(324,366)(325,367)(326,368)(327,369)(328,370)(329,371)
(330,358)(331,359)(332,360)(333,361)(334,362)(335,363)(336,364)(337,351)
(338,352)(339,353)(340,354)(341,355)(342,356)(343,357);;
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*s2*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*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*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 ];;
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)(197,344)(198,350)(199,349)(200,348)(201,347)(202,346)(203,345)
(204,386)(205,392)(206,391)(207,390)(208,389)(209,388)(210,387)(211,379)
(212,385)(213,384)(214,383)(215,382)(216,381)(217,380)(218,372)(219,378)
(220,377)(221,376)(222,375)(223,374)(224,373)(225,365)(226,371)(227,370)
(228,369)(229,368)(230,367)(231,366)(232,358)(233,364)(234,363)(235,362)
(236,361)(237,360)(238,359)(239,351)(240,357)(241,356)(242,355)(243,354)
(244,353)(245,352)(246,295)(247,301)(248,300)(249,299)(250,298)(251,297)
(252,296)(253,337)(254,343)(255,342)(256,341)(257,340)(258,339)(259,338)
(260,330)(261,336)(262,335)(263,334)(264,333)(265,332)(266,331)(267,323)
(268,329)(269,328)(270,327)(271,326)(272,325)(273,324)(274,316)(275,322)
(276,321)(277,320)(278,319)(279,318)(280,317)(281,309)(282,315)(283,314)
(284,313)(285,312)(286,311)(287,310)(288,302)(289,308)(290,307)(291,306)
(292,305)(293,304)(294,303);
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)( 99,303)(100,302)(101,308)(102,307)(103,306)
(104,305)(105,304)(106,296)(107,295)(108,301)(109,300)(110,299)(111,298)
(112,297)(113,338)(114,337)(115,343)(116,342)(117,341)(118,340)(119,339)
(120,331)(121,330)(122,336)(123,335)(124,334)(125,333)(126,332)(127,324)
(128,323)(129,329)(130,328)(131,327)(132,326)(133,325)(134,317)(135,316)
(136,322)(137,321)(138,320)(139,319)(140,318)(141,310)(142,309)(143,315)
(144,314)(145,313)(146,312)(147,311)(148,352)(149,351)(150,357)(151,356)
(152,355)(153,354)(154,353)(155,345)(156,344)(157,350)(158,349)(159,348)
(160,347)(161,346)(162,387)(163,386)(164,392)(165,391)(166,390)(167,389)
(168,388)(169,380)(170,379)(171,385)(172,384)(173,383)(174,382)(175,381)
(176,373)(177,372)(178,378)(179,377)(180,376)(181,375)(182,374)(183,366)
(184,365)(185,371)(186,370)(187,369)(188,368)(189,367)(190,359)(191,358)
(192,364)(193,363)(194,362)(195,361)(196,360);
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)(197,246)(198,247)(199,248)
(200,249)(201,250)(202,251)(203,252)(204,288)(205,289)(206,290)(207,291)
(208,292)(209,293)(210,294)(211,281)(212,282)(213,283)(214,284)(215,285)
(216,286)(217,287)(218,274)(219,275)(220,276)(221,277)(222,278)(223,279)
(224,280)(225,267)(226,268)(227,269)(228,270)(229,271)(230,272)(231,273)
(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,253)
(240,254)(241,255)(242,256)(243,257)(244,258)(245,259)(295,344)(296,345)
(297,346)(298,347)(299,348)(300,349)(301,350)(302,386)(303,387)(304,388)
(305,389)(306,390)(307,391)(308,392)(309,379)(310,380)(311,381)(312,382)
(313,383)(314,384)(315,385)(316,372)(317,373)(318,374)(319,375)(320,376)
(321,377)(322,378)(323,365)(324,366)(325,367)(326,368)(327,369)(328,370)
(329,371)(330,358)(331,359)(332,360)(333,361)(334,362)(335,363)(336,364)
(337,351)(338,352)(339,353)(340,354)(341,355)(342,356)(343,357);
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*s2*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*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*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 >;

References : None.
to this polytope