Polytope of Type {8,14,7}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,14,7}*1568
if this polytope has a name.
Group : SmallGroup(1568,530)
Rank : 4
Schlafli Type : {8,14,7}
Number of vertices, edges, etc : 8, 56, 49, 7
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 : {4,14,7}*784
4-fold quotients : {2,14,7}*392
7-fold quotients : {8,2,7}*224
14-fold quotients : {4,2,7}*112
28-fold quotients : {2,2,7}*56
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 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);;
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)(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);;
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, 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)
(197,198)(199,203)(200,202)(204,240)(205,239)(206,245)(207,244)(208,243)
(209,242)(210,241)(211,233)(212,232)(213,238)(214,237)(215,236)(216,235)
(217,234)(218,226)(219,225)(220,231)(221,230)(222,229)(223,228)(224,227)
(246,247)(248,252)(249,251)(253,289)(254,288)(255,294)(256,293)(257,292)
(258,291)(259,290)(260,282)(261,281)(262,287)(263,286)(264,285)(265,284)
(266,283)(267,275)(268,274)(269,280)(270,279)(271,278)(272,277)(273,276)
(295,296)(297,301)(298,300)(302,338)(303,337)(304,343)(305,342)(306,341)
(307,340)(308,339)(309,331)(310,330)(311,336)(312,335)(313,334)(314,333)
(315,332)(316,324)(317,323)(318,329)(319,328)(320,327)(321,326)(322,325)
(344,345)(346,350)(347,349)(351,387)(352,386)(353,392)(354,391)(355,390)
(356,389)(357,388)(358,380)(359,379)(360,385)(361,384)(362,383)(363,382)
(364,381)(365,373)(366,372)(367,378)(368,377)(369,376)(370,375)(371,374);;
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*s2*s1*s0*s1*s2*s1,
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := 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);
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)(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);
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, 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)(197,198)(199,203)(200,202)(204,240)(205,239)(206,245)(207,244)
(208,243)(209,242)(210,241)(211,233)(212,232)(213,238)(214,237)(215,236)
(216,235)(217,234)(218,226)(219,225)(220,231)(221,230)(222,229)(223,228)
(224,227)(246,247)(248,252)(249,251)(253,289)(254,288)(255,294)(256,293)
(257,292)(258,291)(259,290)(260,282)(261,281)(262,287)(263,286)(264,285)
(265,284)(266,283)(267,275)(268,274)(269,280)(270,279)(271,278)(272,277)
(273,276)(295,296)(297,301)(298,300)(302,338)(303,337)(304,343)(305,342)
(306,341)(307,340)(308,339)(309,331)(310,330)(311,336)(312,335)(313,334)
(314,333)(315,332)(316,324)(317,323)(318,329)(319,328)(320,327)(321,326)
(322,325)(344,345)(346,350)(347,349)(351,387)(352,386)(353,392)(354,391)
(355,390)(356,389)(357,388)(358,380)(359,379)(360,385)(361,384)(362,383)
(363,382)(364,381)(365,373)(366,372)(367,378)(368,377)(369,376)(370,375)
(371,374);
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*s2*s1*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope