Polytope of Type {7,14,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,14,8}*1568
if this polytope has a name.
Group : SmallGroup(1568,530)
Rank : 4
Schlafli Type : {7,14,8}
Number of vertices, edges, etc : 7, 49, 56, 8
Order of s0s1s2s3 : 56
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
4-fold quotients : {7,14,2}*392
7-fold quotients : {7,2,8}*224
14-fold quotients : {7,2,4}*112
28-fold quotients : {7,2,2}*56
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, 9)( 2, 8)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 15, 44)
( 16, 43)( 17, 49)( 18, 48)( 19, 47)( 20, 46)( 21, 45)( 22, 37)( 23, 36)
( 24, 42)( 25, 41)( 26, 40)( 27, 39)( 28, 38)( 29, 30)( 31, 35)( 32, 34)
( 50, 58)( 51, 57)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)( 64, 93)
( 65, 92)( 66, 98)( 67, 97)( 68, 96)( 69, 95)( 70, 94)( 71, 86)( 72, 85)
( 73, 91)( 74, 90)( 75, 89)( 76, 88)( 77, 87)( 78, 79)( 80, 84)( 81, 83)
( 99,107)(100,106)(101,112)(102,111)(103,110)(104,109)(105,108)(113,142)
(114,141)(115,147)(116,146)(117,145)(118,144)(119,143)(120,135)(121,134)
(122,140)(123,139)(124,138)(125,137)(126,136)(127,128)(129,133)(130,132)
(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)(154,157)(162,191)
(163,190)(164,196)(165,195)(166,194)(167,193)(168,192)(169,184)(170,183)
(171,189)(172,188)(173,187)(174,186)(175,185)(176,177)(178,182)(179,181)
(197,205)(198,204)(199,210)(200,209)(201,208)(202,207)(203,206)(211,240)
(212,239)(213,245)(214,244)(215,243)(216,242)(217,241)(218,233)(219,232)
(220,238)(221,237)(222,236)(223,235)(224,234)(225,226)(227,231)(228,230)
(246,254)(247,253)(248,259)(249,258)(250,257)(251,256)(252,255)(260,289)
(261,288)(262,294)(263,293)(264,292)(265,291)(266,290)(267,282)(268,281)
(269,287)(270,286)(271,285)(272,284)(273,283)(274,275)(276,280)(277,279)
(295,303)(296,302)(297,308)(298,307)(299,306)(300,305)(301,304)(309,338)
(310,337)(311,343)(312,342)(313,341)(314,340)(315,339)(316,331)(317,330)
(318,336)(319,335)(320,334)(321,333)(322,332)(323,324)(325,329)(326,328)
(344,352)(345,351)(346,357)(347,356)(348,355)(349,354)(350,353)(358,387)
(359,386)(360,392)(361,391)(362,390)(363,389)(364,388)(365,380)(366,379)
(367,385)(368,384)(369,383)(370,382)(371,381)(372,373)(374,378)(375,377);;
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)(197,295)(198,296)(199,297)(200,298)(201,299)
(202,300)(203,301)(204,337)(205,338)(206,339)(207,340)(208,341)(209,342)
(210,343)(211,330)(212,331)(213,332)(214,333)(215,334)(216,335)(217,336)
(218,323)(219,324)(220,325)(221,326)(222,327)(223,328)(224,329)(225,316)
(226,317)(227,318)(228,319)(229,320)(230,321)(231,322)(232,309)(233,310)
(234,311)(235,312)(236,313)(237,314)(238,315)(239,302)(240,303)(241,304)
(242,305)(243,306)(244,307)(245,308)(246,344)(247,345)(248,346)(249,347)
(250,348)(251,349)(252,350)(253,386)(254,387)(255,388)(256,389)(257,390)
(258,391)(259,392)(260,379)(261,380)(262,381)(263,382)(264,383)(265,384)
(266,385)(267,372)(268,373)(269,374)(270,375)(271,376)(272,377)(273,378)
(274,365)(275,366)(276,367)(277,368)(278,369)(279,370)(280,371)(281,358)
(282,359)(283,360)(284,361)(285,362)(286,363)(287,364)(288,351)(289,352)
(290,353)(291,354)(292,355)(293,356)(294,357);;
s3 := ( 1,197)( 2,198)( 3,199)( 4,200)( 5,201)( 6,202)( 7,203)( 8,204)
( 9,205)( 10,206)( 11,207)( 12,208)( 13,209)( 14,210)( 15,211)( 16,212)
( 17,213)( 18,214)( 19,215)( 20,216)( 21,217)( 22,218)( 23,219)( 24,220)
( 25,221)( 26,222)( 27,223)( 28,224)( 29,225)( 30,226)( 31,227)( 32,228)
( 33,229)( 34,230)( 35,231)( 36,232)( 37,233)( 38,234)( 39,235)( 40,236)
( 41,237)( 42,238)( 43,239)( 44,240)( 45,241)( 46,242)( 47,243)( 48,244)
( 49,245)( 50,246)( 51,247)( 52,248)( 53,249)( 54,250)( 55,251)( 56,252)
( 57,253)( 58,254)( 59,255)( 60,256)( 61,257)( 62,258)( 63,259)( 64,260)
( 65,261)( 66,262)( 67,263)( 68,264)( 69,265)( 70,266)( 71,267)( 72,268)
( 73,269)( 74,270)( 75,271)( 76,272)( 77,273)( 78,274)( 79,275)( 80,276)
( 81,277)( 82,278)( 83,279)( 84,280)( 85,281)( 86,282)( 87,283)( 88,284)
( 89,285)( 90,286)( 91,287)( 92,288)( 93,289)( 94,290)( 95,291)( 96,292)
( 97,293)( 98,294)( 99,344)(100,345)(101,346)(102,347)(103,348)(104,349)
(105,350)(106,351)(107,352)(108,353)(109,354)(110,355)(111,356)(112,357)
(113,358)(114,359)(115,360)(116,361)(117,362)(118,363)(119,364)(120,365)
(121,366)(122,367)(123,368)(124,369)(125,370)(126,371)(127,372)(128,373)
(129,374)(130,375)(131,376)(132,377)(133,378)(134,379)(135,380)(136,381)
(137,382)(138,383)(139,384)(140,385)(141,386)(142,387)(143,388)(144,389)
(145,390)(146,391)(147,392)(148,295)(149,296)(150,297)(151,298)(152,299)
(153,300)(154,301)(155,302)(156,303)(157,304)(158,305)(159,306)(160,307)
(161,308)(162,309)(163,310)(164,311)(165,312)(166,313)(167,314)(168,315)
(169,316)(170,317)(171,318)(172,319)(173,320)(174,321)(175,322)(176,323)
(177,324)(178,325)(179,326)(180,327)(181,328)(182,329)(183,330)(184,331)
(185,332)(186,333)(187,334)(188,335)(189,336)(190,337)(191,338)(192,339)
(193,340)(194,341)(195,342)(196,343);;
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*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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)!( 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, 9)( 2, 8)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 10)
( 15, 44)( 16, 43)( 17, 49)( 18, 48)( 19, 47)( 20, 46)( 21, 45)( 22, 37)
( 23, 36)( 24, 42)( 25, 41)( 26, 40)( 27, 39)( 28, 38)( 29, 30)( 31, 35)
( 32, 34)( 50, 58)( 51, 57)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)
( 64, 93)( 65, 92)( 66, 98)( 67, 97)( 68, 96)( 69, 95)( 70, 94)( 71, 86)
( 72, 85)( 73, 91)( 74, 90)( 75, 89)( 76, 88)( 77, 87)( 78, 79)( 80, 84)
( 81, 83)( 99,107)(100,106)(101,112)(102,111)(103,110)(104,109)(105,108)
(113,142)(114,141)(115,147)(116,146)(117,145)(118,144)(119,143)(120,135)
(121,134)(122,140)(123,139)(124,138)(125,137)(126,136)(127,128)(129,133)
(130,132)(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)(154,157)
(162,191)(163,190)(164,196)(165,195)(166,194)(167,193)(168,192)(169,184)
(170,183)(171,189)(172,188)(173,187)(174,186)(175,185)(176,177)(178,182)
(179,181)(197,205)(198,204)(199,210)(200,209)(201,208)(202,207)(203,206)
(211,240)(212,239)(213,245)(214,244)(215,243)(216,242)(217,241)(218,233)
(219,232)(220,238)(221,237)(222,236)(223,235)(224,234)(225,226)(227,231)
(228,230)(246,254)(247,253)(248,259)(249,258)(250,257)(251,256)(252,255)
(260,289)(261,288)(262,294)(263,293)(264,292)(265,291)(266,290)(267,282)
(268,281)(269,287)(270,286)(271,285)(272,284)(273,283)(274,275)(276,280)
(277,279)(295,303)(296,302)(297,308)(298,307)(299,306)(300,305)(301,304)
(309,338)(310,337)(311,343)(312,342)(313,341)(314,340)(315,339)(316,331)
(317,330)(318,336)(319,335)(320,334)(321,333)(322,332)(323,324)(325,329)
(326,328)(344,352)(345,351)(346,357)(347,356)(348,355)(349,354)(350,353)
(358,387)(359,386)(360,392)(361,391)(362,390)(363,389)(364,388)(365,380)
(366,379)(367,385)(368,384)(369,383)(370,382)(371,381)(372,373)(374,378)
(375,377);
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)(197,295)(198,296)(199,297)(200,298)
(201,299)(202,300)(203,301)(204,337)(205,338)(206,339)(207,340)(208,341)
(209,342)(210,343)(211,330)(212,331)(213,332)(214,333)(215,334)(216,335)
(217,336)(218,323)(219,324)(220,325)(221,326)(222,327)(223,328)(224,329)
(225,316)(226,317)(227,318)(228,319)(229,320)(230,321)(231,322)(232,309)
(233,310)(234,311)(235,312)(236,313)(237,314)(238,315)(239,302)(240,303)
(241,304)(242,305)(243,306)(244,307)(245,308)(246,344)(247,345)(248,346)
(249,347)(250,348)(251,349)(252,350)(253,386)(254,387)(255,388)(256,389)
(257,390)(258,391)(259,392)(260,379)(261,380)(262,381)(263,382)(264,383)
(265,384)(266,385)(267,372)(268,373)(269,374)(270,375)(271,376)(272,377)
(273,378)(274,365)(275,366)(276,367)(277,368)(278,369)(279,370)(280,371)
(281,358)(282,359)(283,360)(284,361)(285,362)(286,363)(287,364)(288,351)
(289,352)(290,353)(291,354)(292,355)(293,356)(294,357);
s3 := Sym(392)!( 1,197)( 2,198)( 3,199)( 4,200)( 5,201)( 6,202)( 7,203)
( 8,204)( 9,205)( 10,206)( 11,207)( 12,208)( 13,209)( 14,210)( 15,211)
( 16,212)( 17,213)( 18,214)( 19,215)( 20,216)( 21,217)( 22,218)( 23,219)
( 24,220)( 25,221)( 26,222)( 27,223)( 28,224)( 29,225)( 30,226)( 31,227)
( 32,228)( 33,229)( 34,230)( 35,231)( 36,232)( 37,233)( 38,234)( 39,235)
( 40,236)( 41,237)( 42,238)( 43,239)( 44,240)( 45,241)( 46,242)( 47,243)
( 48,244)( 49,245)( 50,246)( 51,247)( 52,248)( 53,249)( 54,250)( 55,251)
( 56,252)( 57,253)( 58,254)( 59,255)( 60,256)( 61,257)( 62,258)( 63,259)
( 64,260)( 65,261)( 66,262)( 67,263)( 68,264)( 69,265)( 70,266)( 71,267)
( 72,268)( 73,269)( 74,270)( 75,271)( 76,272)( 77,273)( 78,274)( 79,275)
( 80,276)( 81,277)( 82,278)( 83,279)( 84,280)( 85,281)( 86,282)( 87,283)
( 88,284)( 89,285)( 90,286)( 91,287)( 92,288)( 93,289)( 94,290)( 95,291)
( 96,292)( 97,293)( 98,294)( 99,344)(100,345)(101,346)(102,347)(103,348)
(104,349)(105,350)(106,351)(107,352)(108,353)(109,354)(110,355)(111,356)
(112,357)(113,358)(114,359)(115,360)(116,361)(117,362)(118,363)(119,364)
(120,365)(121,366)(122,367)(123,368)(124,369)(125,370)(126,371)(127,372)
(128,373)(129,374)(130,375)(131,376)(132,377)(133,378)(134,379)(135,380)
(136,381)(137,382)(138,383)(139,384)(140,385)(141,386)(142,387)(143,388)
(144,389)(145,390)(146,391)(147,392)(148,295)(149,296)(150,297)(151,298)
(152,299)(153,300)(154,301)(155,302)(156,303)(157,304)(158,305)(159,306)
(160,307)(161,308)(162,309)(163,310)(164,311)(165,312)(166,313)(167,314)
(168,315)(169,316)(170,317)(171,318)(172,319)(173,320)(174,321)(175,322)
(176,323)(177,324)(178,325)(179,326)(180,327)(181,328)(182,329)(183,330)
(184,331)(185,332)(186,333)(187,334)(188,335)(189,336)(190,337)(191,338)
(192,339)(193,340)(194,341)(195,342)(196,343);
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*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope