Polytope of Type {14,14,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,14,4}*1568c
if this polytope has a name.
Group : SmallGroup(1568,877)
Rank : 4
Schlafli Type : {14,14,4}
Number of vertices, edges, etc : 14, 98, 28, 4
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 : {7,14,4}*784, {14,14,2}*784c
4-fold quotients : {7,14,2}*392
7-fold quotients : {14,2,4}*224
14-fold quotients : {7,2,4}*112, {14,2,2}*112
28-fold quotients : {7,2,2}*56
49-fold quotients : {2,2,4}*32
98-fold quotients : {2,2,2}*16
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)
(198,203)(199,202)(200,201)(204,239)(205,245)(206,244)(207,243)(208,242)
(209,241)(210,240)(211,232)(212,238)(213,237)(214,236)(215,235)(216,234)
(217,233)(218,225)(219,231)(220,230)(221,229)(222,228)(223,227)(224,226)
(247,252)(248,251)(249,250)(253,288)(254,294)(255,293)(256,292)(257,291)
(258,290)(259,289)(260,281)(261,287)(262,286)(263,285)(264,284)(265,283)
(266,282)(267,274)(268,280)(269,279)(270,278)(271,277)(272,276)(273,275)
(296,301)(297,300)(298,299)(302,337)(303,343)(304,342)(305,341)(306,340)
(307,339)(308,338)(309,330)(310,336)(311,335)(312,334)(313,333)(314,332)
(315,331)(316,323)(317,329)(318,328)(319,327)(320,326)(321,325)(322,324)
(345,350)(346,349)(347,348)(351,386)(352,392)(353,391)(354,390)(355,389)
(356,388)(357,387)(358,379)(359,385)(360,384)(361,383)(362,382)(363,381)
(364,380)(365,372)(366,378)(367,377)(368,376)(369,375)(370,374)(371,373);;
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)( 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);;
s3 := ( 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);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, 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*s2*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 ];;
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)(198,203)(199,202)(200,201)(204,239)(205,245)(206,244)(207,243)
(208,242)(209,241)(210,240)(211,232)(212,238)(213,237)(214,236)(215,235)
(216,234)(217,233)(218,225)(219,231)(220,230)(221,229)(222,228)(223,227)
(224,226)(247,252)(248,251)(249,250)(253,288)(254,294)(255,293)(256,292)
(257,291)(258,290)(259,289)(260,281)(261,287)(262,286)(263,285)(264,284)
(265,283)(266,282)(267,274)(268,280)(269,279)(270,278)(271,277)(272,276)
(273,275)(296,301)(297,300)(298,299)(302,337)(303,343)(304,342)(305,341)
(306,340)(307,339)(308,338)(309,330)(310,336)(311,335)(312,334)(313,333)
(314,332)(315,331)(316,323)(317,329)(318,328)(319,327)(320,326)(321,325)
(322,324)(345,350)(346,349)(347,348)(351,386)(352,392)(353,391)(354,390)
(355,389)(356,388)(357,387)(358,379)(359,385)(360,384)(361,383)(362,382)
(363,381)(364,380)(365,372)(366,378)(367,377)(368,376)(369,375)(370,374)
(371,373);
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)( 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);
s3 := 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);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
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*s2*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 >;
References : None.
to this polytope