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