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