Polytope of Type {4,14,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,14,14}*1568c
if this polytope has a name.
Group : SmallGroup(1568,877)
Rank : 4
Schlafli Type : {4,14,14}
Number of vertices, edges, etc : 4, 28, 98, 14
Order of s0s1s2s3 : 28
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {4,14,7}*784, {2,14,14}*784b
4-fold quotients : {2,14,7}*392
7-fold quotients : {4,2,14}*224
14-fold quotients : {4,2,7}*112, {2,2,14}*112
28-fold quotients : {2,2,7}*56
49-fold quotients : {4,2,2}*32
98-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1, 99)( 2,100)( 3,101)( 4,102)( 5,103)( 6,104)( 7,105)( 8,106)
( 9,107)( 10,108)( 11,109)( 12,110)( 13,111)( 14,112)( 15,113)( 16,114)
( 17,115)( 18,116)( 19,117)( 20,118)( 21,119)( 22,120)( 23,121)( 24,122)
( 25,123)( 26,124)( 27,125)( 28,126)( 29,127)( 30,128)( 31,129)( 32,130)
( 33,131)( 34,132)( 35,133)( 36,134)( 37,135)( 38,136)( 39,137)( 40,138)
( 41,139)( 42,140)( 43,141)( 44,142)( 45,143)( 46,144)( 47,145)( 48,146)
( 49,147)( 50,148)( 51,149)( 52,150)( 53,151)( 54,152)( 55,153)( 56,154)
( 57,155)( 58,156)( 59,157)( 60,158)( 61,159)( 62,160)( 63,161)( 64,162)
( 65,163)( 66,164)( 67,165)( 68,166)( 69,167)( 70,168)( 71,169)( 72,170)
( 73,171)( 74,172)( 75,173)( 76,174)( 77,175)( 78,176)( 79,177)( 80,178)
( 81,179)( 82,180)( 83,181)( 84,182)( 85,183)( 86,184)( 87,185)( 88,186)
( 89,187)( 90,188)( 91,189)( 92,190)( 93,191)( 94,192)( 95,193)( 96,194)
( 97,195)( 98,196)(197,295)(198,296)(199,297)(200,298)(201,299)(202,300)
(203,301)(204,302)(205,303)(206,304)(207,305)(208,306)(209,307)(210,308)
(211,309)(212,310)(213,311)(214,312)(215,313)(216,314)(217,315)(218,316)
(219,317)(220,318)(221,319)(222,320)(223,321)(224,322)(225,323)(226,324)
(227,325)(228,326)(229,327)(230,328)(231,329)(232,330)(233,331)(234,332)
(235,333)(236,334)(237,335)(238,336)(239,337)(240,338)(241,339)(242,340)
(243,341)(244,342)(245,343)(246,344)(247,345)(248,346)(249,347)(250,348)
(251,349)(252,350)(253,351)(254,352)(255,353)(256,354)(257,355)(258,356)
(259,357)(260,358)(261,359)(262,360)(263,361)(264,362)(265,363)(266,364)
(267,365)(268,366)(269,367)(270,368)(271,369)(272,370)(273,371)(274,372)
(275,373)(276,374)(277,375)(278,376)(279,377)(280,378)(281,379)(282,380)
(283,381)(284,382)(285,383)(286,384)(287,385)(288,386)(289,387)(290,388)
(291,389)(292,390)(293,391)(294,392);;
s1 := ( 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)(204,239)(205,240)(206,241)(207,242)(208,243)
(209,244)(210,245)(211,232)(212,233)(213,234)(214,235)(215,236)(216,237)
(217,238)(218,225)(219,226)(220,227)(221,228)(222,229)(223,230)(224,231)
(253,288)(254,289)(255,290)(256,291)(257,292)(258,293)(259,294)(260,281)
(261,282)(262,283)(263,284)(264,285)(265,286)(266,287)(267,274)(268,275)
(269,276)(270,277)(271,278)(272,279)(273,280)(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);;
s2 := ( 1, 8)( 2, 14)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)( 15, 43)
( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)( 23, 42)
( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)( 32, 33)
( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)( 64, 92)
( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)( 72, 91)
( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)( 81, 82)
( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)(113,141)
(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,134)(121,140)
(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)(130,131)
(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)(162,190)
(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,183)(170,189)
(171,188)(172,187)(173,186)(174,185)(175,184)(177,182)(178,181)(179,180)
(197,204)(198,210)(199,209)(200,208)(201,207)(202,206)(203,205)(211,239)
(212,245)(213,244)(214,243)(215,242)(216,241)(217,240)(218,232)(219,238)
(220,237)(221,236)(222,235)(223,234)(224,233)(226,231)(227,230)(228,229)
(246,253)(247,259)(248,258)(249,257)(250,256)(251,255)(252,254)(260,288)
(261,294)(262,293)(263,292)(264,291)(265,290)(266,289)(267,281)(268,287)
(269,286)(270,285)(271,284)(272,283)(273,282)(275,280)(276,279)(277,278)
(295,302)(296,308)(297,307)(298,306)(299,305)(300,304)(301,303)(309,337)
(310,343)(311,342)(312,341)(313,340)(314,339)(315,338)(316,330)(317,336)
(318,335)(319,334)(320,333)(321,332)(322,331)(324,329)(325,328)(326,327)
(344,351)(345,357)(346,356)(347,355)(348,354)(349,353)(350,352)(358,386)
(359,392)(360,391)(361,390)(362,389)(363,388)(364,387)(365,379)(366,385)
(367,384)(368,383)(369,382)(370,381)(371,380)(373,378)(374,377)(375,376);;
s3 := ( 1,198)( 2,197)( 3,203)( 4,202)( 5,201)( 6,200)( 7,199)( 8,240)
( 9,239)( 10,245)( 11,244)( 12,243)( 13,242)( 14,241)( 15,233)( 16,232)
( 17,238)( 18,237)( 19,236)( 20,235)( 21,234)( 22,226)( 23,225)( 24,231)
( 25,230)( 26,229)( 27,228)( 28,227)( 29,219)( 30,218)( 31,224)( 32,223)
( 33,222)( 34,221)( 35,220)( 36,212)( 37,211)( 38,217)( 39,216)( 40,215)
( 41,214)( 42,213)( 43,205)( 44,204)( 45,210)( 46,209)( 47,208)( 48,207)
( 49,206)( 50,247)( 51,246)( 52,252)( 53,251)( 54,250)( 55,249)( 56,248)
( 57,289)( 58,288)( 59,294)( 60,293)( 61,292)( 62,291)( 63,290)( 64,282)
( 65,281)( 66,287)( 67,286)( 68,285)( 69,284)( 70,283)( 71,275)( 72,274)
( 73,280)( 74,279)( 75,278)( 76,277)( 77,276)( 78,268)( 79,267)( 80,273)
( 81,272)( 82,271)( 83,270)( 84,269)( 85,261)( 86,260)( 87,266)( 88,265)
( 89,264)( 90,263)( 91,262)( 92,254)( 93,253)( 94,259)( 95,258)( 96,257)
( 97,256)( 98,255)( 99,296)(100,295)(101,301)(102,300)(103,299)(104,298)
(105,297)(106,338)(107,337)(108,343)(109,342)(110,341)(111,340)(112,339)
(113,331)(114,330)(115,336)(116,335)(117,334)(118,333)(119,332)(120,324)
(121,323)(122,329)(123,328)(124,327)(125,326)(126,325)(127,317)(128,316)
(129,322)(130,321)(131,320)(132,319)(133,318)(134,310)(135,309)(136,315)
(137,314)(138,313)(139,312)(140,311)(141,303)(142,302)(143,308)(144,307)
(145,306)(146,305)(147,304)(148,345)(149,344)(150,350)(151,349)(152,348)
(153,347)(154,346)(155,387)(156,386)(157,392)(158,391)(159,390)(160,389)
(161,388)(162,380)(163,379)(164,385)(165,384)(166,383)(167,382)(168,381)
(169,373)(170,372)(171,378)(172,377)(173,376)(174,375)(175,374)(176,366)
(177,365)(178,371)(179,370)(180,369)(181,368)(182,367)(183,359)(184,358)
(185,364)(186,363)(187,362)(188,361)(189,360)(190,352)(191,351)(192,357)
(193,356)(194,355)(195,354)(196,353);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(392)!( 1, 99)( 2,100)( 3,101)( 4,102)( 5,103)( 6,104)( 7,105)
( 8,106)( 9,107)( 10,108)( 11,109)( 12,110)( 13,111)( 14,112)( 15,113)
( 16,114)( 17,115)( 18,116)( 19,117)( 20,118)( 21,119)( 22,120)( 23,121)
( 24,122)( 25,123)( 26,124)( 27,125)( 28,126)( 29,127)( 30,128)( 31,129)
( 32,130)( 33,131)( 34,132)( 35,133)( 36,134)( 37,135)( 38,136)( 39,137)
( 40,138)( 41,139)( 42,140)( 43,141)( 44,142)( 45,143)( 46,144)( 47,145)
( 48,146)( 49,147)( 50,148)( 51,149)( 52,150)( 53,151)( 54,152)( 55,153)
( 56,154)( 57,155)( 58,156)( 59,157)( 60,158)( 61,159)( 62,160)( 63,161)
( 64,162)( 65,163)( 66,164)( 67,165)( 68,166)( 69,167)( 70,168)( 71,169)
( 72,170)( 73,171)( 74,172)( 75,173)( 76,174)( 77,175)( 78,176)( 79,177)
( 80,178)( 81,179)( 82,180)( 83,181)( 84,182)( 85,183)( 86,184)( 87,185)
( 88,186)( 89,187)( 90,188)( 91,189)( 92,190)( 93,191)( 94,192)( 95,193)
( 96,194)( 97,195)( 98,196)(197,295)(198,296)(199,297)(200,298)(201,299)
(202,300)(203,301)(204,302)(205,303)(206,304)(207,305)(208,306)(209,307)
(210,308)(211,309)(212,310)(213,311)(214,312)(215,313)(216,314)(217,315)
(218,316)(219,317)(220,318)(221,319)(222,320)(223,321)(224,322)(225,323)
(226,324)(227,325)(228,326)(229,327)(230,328)(231,329)(232,330)(233,331)
(234,332)(235,333)(236,334)(237,335)(238,336)(239,337)(240,338)(241,339)
(242,340)(243,341)(244,342)(245,343)(246,344)(247,345)(248,346)(249,347)
(250,348)(251,349)(252,350)(253,351)(254,352)(255,353)(256,354)(257,355)
(258,356)(259,357)(260,358)(261,359)(262,360)(263,361)(264,362)(265,363)
(266,364)(267,365)(268,366)(269,367)(270,368)(271,369)(272,370)(273,371)
(274,372)(275,373)(276,374)(277,375)(278,376)(279,377)(280,378)(281,379)
(282,380)(283,381)(284,382)(285,383)(286,384)(287,385)(288,386)(289,387)
(290,388)(291,389)(292,390)(293,391)(294,392);
s1 := 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)(204,239)(205,240)(206,241)(207,242)
(208,243)(209,244)(210,245)(211,232)(212,233)(213,234)(214,235)(215,236)
(216,237)(217,238)(218,225)(219,226)(220,227)(221,228)(222,229)(223,230)
(224,231)(253,288)(254,289)(255,290)(256,291)(257,292)(258,293)(259,294)
(260,281)(261,282)(262,283)(263,284)(264,285)(265,286)(266,287)(267,274)
(268,275)(269,276)(270,277)(271,278)(272,279)(273,280)(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);
s2 := Sym(392)!( 1, 8)( 2, 14)( 3, 13)( 4, 12)( 5, 11)( 6, 10)( 7, 9)
( 15, 43)( 16, 49)( 17, 48)( 18, 47)( 19, 46)( 20, 45)( 21, 44)( 22, 36)
( 23, 42)( 24, 41)( 25, 40)( 26, 39)( 27, 38)( 28, 37)( 30, 35)( 31, 34)
( 32, 33)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)( 55, 59)( 56, 58)
( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71, 85)
( 72, 91)( 73, 90)( 74, 89)( 75, 88)( 76, 87)( 77, 86)( 79, 84)( 80, 83)
( 81, 82)( 99,106)(100,112)(101,111)(102,110)(103,109)(104,108)(105,107)
(113,141)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,134)
(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)
(130,131)(148,155)(149,161)(150,160)(151,159)(152,158)(153,157)(154,156)
(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)(169,183)
(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(177,182)(178,181)
(179,180)(197,204)(198,210)(199,209)(200,208)(201,207)(202,206)(203,205)
(211,239)(212,245)(213,244)(214,243)(215,242)(216,241)(217,240)(218,232)
(219,238)(220,237)(221,236)(222,235)(223,234)(224,233)(226,231)(227,230)
(228,229)(246,253)(247,259)(248,258)(249,257)(250,256)(251,255)(252,254)
(260,288)(261,294)(262,293)(263,292)(264,291)(265,290)(266,289)(267,281)
(268,287)(269,286)(270,285)(271,284)(272,283)(273,282)(275,280)(276,279)
(277,278)(295,302)(296,308)(297,307)(298,306)(299,305)(300,304)(301,303)
(309,337)(310,343)(311,342)(312,341)(313,340)(314,339)(315,338)(316,330)
(317,336)(318,335)(319,334)(320,333)(321,332)(322,331)(324,329)(325,328)
(326,327)(344,351)(345,357)(346,356)(347,355)(348,354)(349,353)(350,352)
(358,386)(359,392)(360,391)(361,390)(362,389)(363,388)(364,387)(365,379)
(366,385)(367,384)(368,383)(369,382)(370,381)(371,380)(373,378)(374,377)
(375,376);
s3 := Sym(392)!( 1,198)( 2,197)( 3,203)( 4,202)( 5,201)( 6,200)( 7,199)
( 8,240)( 9,239)( 10,245)( 11,244)( 12,243)( 13,242)( 14,241)( 15,233)
( 16,232)( 17,238)( 18,237)( 19,236)( 20,235)( 21,234)( 22,226)( 23,225)
( 24,231)( 25,230)( 26,229)( 27,228)( 28,227)( 29,219)( 30,218)( 31,224)
( 32,223)( 33,222)( 34,221)( 35,220)( 36,212)( 37,211)( 38,217)( 39,216)
( 40,215)( 41,214)( 42,213)( 43,205)( 44,204)( 45,210)( 46,209)( 47,208)
( 48,207)( 49,206)( 50,247)( 51,246)( 52,252)( 53,251)( 54,250)( 55,249)
( 56,248)( 57,289)( 58,288)( 59,294)( 60,293)( 61,292)( 62,291)( 63,290)
( 64,282)( 65,281)( 66,287)( 67,286)( 68,285)( 69,284)( 70,283)( 71,275)
( 72,274)( 73,280)( 74,279)( 75,278)( 76,277)( 77,276)( 78,268)( 79,267)
( 80,273)( 81,272)( 82,271)( 83,270)( 84,269)( 85,261)( 86,260)( 87,266)
( 88,265)( 89,264)( 90,263)( 91,262)( 92,254)( 93,253)( 94,259)( 95,258)
( 96,257)( 97,256)( 98,255)( 99,296)(100,295)(101,301)(102,300)(103,299)
(104,298)(105,297)(106,338)(107,337)(108,343)(109,342)(110,341)(111,340)
(112,339)(113,331)(114,330)(115,336)(116,335)(117,334)(118,333)(119,332)
(120,324)(121,323)(122,329)(123,328)(124,327)(125,326)(126,325)(127,317)
(128,316)(129,322)(130,321)(131,320)(132,319)(133,318)(134,310)(135,309)
(136,315)(137,314)(138,313)(139,312)(140,311)(141,303)(142,302)(143,308)
(144,307)(145,306)(146,305)(147,304)(148,345)(149,344)(150,350)(151,349)
(152,348)(153,347)(154,346)(155,387)(156,386)(157,392)(158,391)(159,390)
(160,389)(161,388)(162,380)(163,379)(164,385)(165,384)(166,383)(167,382)
(168,381)(169,373)(170,372)(171,378)(172,377)(173,376)(174,375)(175,374)
(176,366)(177,365)(178,371)(179,370)(180,369)(181,368)(182,367)(183,359)
(184,358)(185,364)(186,363)(187,362)(188,361)(189,360)(190,352)(191,351)
(192,357)(193,356)(194,355)(195,354)(196,353);
poly := sub<Sym(392)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope