Polytope of Type {14,8,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,8,3}*1344
if this polytope has a name.
Group : SmallGroup(1344,11355)
Rank : 4
Schlafli Type : {14,8,3}
Number of vertices, edges, etc : 14, 112, 24, 6
Order of s0s1s2s3 : 84
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 : {14,4,3}*672
7-fold quotients : {2,8,3}*192
8-fold quotients : {14,2,3}*168
14-fold quotients : {2,4,3}*96
16-fold quotients : {7,2,3}*84
28-fold quotients : {2,4,3}*48
56-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 9, 49)( 10, 50)( 11, 51)( 12, 52)( 13, 53)( 14, 54)( 15, 55)( 16, 56)
( 17, 41)( 18, 42)( 19, 43)( 20, 44)( 21, 45)( 22, 46)( 23, 47)( 24, 48)
( 25, 33)( 26, 34)( 27, 35)( 28, 36)( 29, 37)( 30, 38)( 31, 39)( 32, 40)
( 65,105)( 66,106)( 67,107)( 68,108)( 69,109)( 70,110)( 71,111)( 72,112)
( 73, 97)( 74, 98)( 75, 99)( 76,100)( 77,101)( 78,102)( 79,103)( 80,104)
( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)
(121,161)(122,162)(123,163)(124,164)(125,165)(126,166)(127,167)(128,168)
(129,153)(130,154)(131,155)(132,156)(133,157)(134,158)(135,159)(136,160)
(137,145)(138,146)(139,147)(140,148)(141,149)(142,150)(143,151)(144,152)
(177,217)(178,218)(179,219)(180,220)(181,221)(182,222)(183,223)(184,224)
(185,209)(186,210)(187,211)(188,212)(189,213)(190,214)(191,215)(192,216)
(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)(200,208)
(233,273)(234,274)(235,275)(236,276)(237,277)(238,278)(239,279)(240,280)
(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)(248,272)
(249,257)(250,258)(251,259)(252,260)(253,261)(254,262)(255,263)(256,264)
(289,329)(290,330)(291,331)(292,332)(293,333)(294,334)(295,335)(296,336)
(297,321)(298,322)(299,323)(300,324)(301,325)(302,326)(303,327)(304,328)
(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)(312,320);;
s1 := ( 1,181)( 2,182)( 3,184)( 4,183)( 5,178)( 6,177)( 7,179)( 8,180)
( 9,173)( 10,174)( 11,176)( 12,175)( 13,170)( 14,169)( 15,171)( 16,172)
( 17,221)( 18,222)( 19,224)( 20,223)( 21,218)( 22,217)( 23,219)( 24,220)
( 25,213)( 26,214)( 27,216)( 28,215)( 29,210)( 30,209)( 31,211)( 32,212)
( 33,205)( 34,206)( 35,208)( 36,207)( 37,202)( 38,201)( 39,203)( 40,204)
( 41,197)( 42,198)( 43,200)( 44,199)( 45,194)( 46,193)( 47,195)( 48,196)
( 49,189)( 50,190)( 51,192)( 52,191)( 53,186)( 54,185)( 55,187)( 56,188)
( 57,237)( 58,238)( 59,240)( 60,239)( 61,234)( 62,233)( 63,235)( 64,236)
( 65,229)( 66,230)( 67,232)( 68,231)( 69,226)( 70,225)( 71,227)( 72,228)
( 73,277)( 74,278)( 75,280)( 76,279)( 77,274)( 78,273)( 79,275)( 80,276)
( 81,269)( 82,270)( 83,272)( 84,271)( 85,266)( 86,265)( 87,267)( 88,268)
( 89,261)( 90,262)( 91,264)( 92,263)( 93,258)( 94,257)( 95,259)( 96,260)
( 97,253)( 98,254)( 99,256)(100,255)(101,250)(102,249)(103,251)(104,252)
(105,245)(106,246)(107,248)(108,247)(109,242)(110,241)(111,243)(112,244)
(113,293)(114,294)(115,296)(116,295)(117,290)(118,289)(119,291)(120,292)
(121,285)(122,286)(123,288)(124,287)(125,282)(126,281)(127,283)(128,284)
(129,333)(130,334)(131,336)(132,335)(133,330)(134,329)(135,331)(136,332)
(137,325)(138,326)(139,328)(140,327)(141,322)(142,321)(143,323)(144,324)
(145,317)(146,318)(147,320)(148,319)(149,314)(150,313)(151,315)(152,316)
(153,309)(154,310)(155,312)(156,311)(157,306)(158,305)(159,307)(160,308)
(161,301)(162,302)(163,304)(164,303)(165,298)(166,297)(167,299)(168,300);;
s2 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)
( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 43, 44)
( 45, 47)( 46, 48)( 51, 52)( 53, 55)( 54, 56)( 57,113)( 58,114)( 59,116)
( 60,115)( 61,119)( 62,120)( 63,117)( 64,118)( 65,121)( 66,122)( 67,124)
( 68,123)( 69,127)( 70,128)( 71,125)( 72,126)( 73,129)( 74,130)( 75,132)
( 76,131)( 77,135)( 78,136)( 79,133)( 80,134)( 81,137)( 82,138)( 83,140)
( 84,139)( 85,143)( 86,144)( 87,141)( 88,142)( 89,145)( 90,146)( 91,148)
( 92,147)( 93,151)( 94,152)( 95,149)( 96,150)( 97,153)( 98,154)( 99,156)
(100,155)(101,159)(102,160)(103,157)(104,158)(105,161)(106,162)(107,164)
(108,163)(109,167)(110,168)(111,165)(112,166)(169,170)(173,176)(174,175)
(177,178)(181,184)(182,183)(185,186)(189,192)(190,191)(193,194)(197,200)
(198,199)(201,202)(205,208)(206,207)(209,210)(213,216)(214,215)(217,218)
(221,224)(222,223)(225,282)(226,281)(227,283)(228,284)(229,288)(230,287)
(231,286)(232,285)(233,290)(234,289)(235,291)(236,292)(237,296)(238,295)
(239,294)(240,293)(241,298)(242,297)(243,299)(244,300)(245,304)(246,303)
(247,302)(248,301)(249,306)(250,305)(251,307)(252,308)(253,312)(254,311)
(255,310)(256,309)(257,314)(258,313)(259,315)(260,316)(261,320)(262,319)
(263,318)(264,317)(265,322)(266,321)(267,323)(268,324)(269,328)(270,327)
(271,326)(272,325)(273,330)(274,329)(275,331)(276,332)(277,336)(278,335)
(279,334)(280,333);;
s3 := ( 1, 57)( 2, 58)( 3, 63)( 4, 64)( 5, 62)( 6, 61)( 7, 59)( 8, 60)
( 9, 65)( 10, 66)( 11, 71)( 12, 72)( 13, 70)( 14, 69)( 15, 67)( 16, 68)
( 17, 73)( 18, 74)( 19, 79)( 20, 80)( 21, 78)( 22, 77)( 23, 75)( 24, 76)
( 25, 81)( 26, 82)( 27, 87)( 28, 88)( 29, 86)( 30, 85)( 31, 83)( 32, 84)
( 33, 89)( 34, 90)( 35, 95)( 36, 96)( 37, 94)( 38, 93)( 39, 91)( 40, 92)
( 41, 97)( 42, 98)( 43,103)( 44,104)( 45,102)( 46,101)( 47, 99)( 48,100)
( 49,105)( 50,106)( 51,111)( 52,112)( 53,110)( 54,109)( 55,107)( 56,108)
(115,119)(116,120)(117,118)(123,127)(124,128)(125,126)(131,135)(132,136)
(133,134)(139,143)(140,144)(141,142)(147,151)(148,152)(149,150)(155,159)
(156,160)(157,158)(163,167)(164,168)(165,166)(169,226)(170,225)(171,232)
(172,231)(173,229)(174,230)(175,228)(176,227)(177,234)(178,233)(179,240)
(180,239)(181,237)(182,238)(183,236)(184,235)(185,242)(186,241)(187,248)
(188,247)(189,245)(190,246)(191,244)(192,243)(193,250)(194,249)(195,256)
(196,255)(197,253)(198,254)(199,252)(200,251)(201,258)(202,257)(203,264)
(204,263)(205,261)(206,262)(207,260)(208,259)(209,266)(210,265)(211,272)
(212,271)(213,269)(214,270)(215,268)(216,267)(217,274)(218,273)(219,280)
(220,279)(221,277)(222,278)(223,276)(224,275)(281,282)(283,288)(284,287)
(289,290)(291,296)(292,295)(297,298)(299,304)(300,303)(305,306)(307,312)
(308,311)(313,314)(315,320)(316,319)(321,322)(323,328)(324,327)(329,330)
(331,336)(332,335);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(336)!( 9, 49)( 10, 50)( 11, 51)( 12, 52)( 13, 53)( 14, 54)( 15, 55)
( 16, 56)( 17, 41)( 18, 42)( 19, 43)( 20, 44)( 21, 45)( 22, 46)( 23, 47)
( 24, 48)( 25, 33)( 26, 34)( 27, 35)( 28, 36)( 29, 37)( 30, 38)( 31, 39)
( 32, 40)( 65,105)( 66,106)( 67,107)( 68,108)( 69,109)( 70,110)( 71,111)
( 72,112)( 73, 97)( 74, 98)( 75, 99)( 76,100)( 77,101)( 78,102)( 79,103)
( 80,104)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)
( 88, 96)(121,161)(122,162)(123,163)(124,164)(125,165)(126,166)(127,167)
(128,168)(129,153)(130,154)(131,155)(132,156)(133,157)(134,158)(135,159)
(136,160)(137,145)(138,146)(139,147)(140,148)(141,149)(142,150)(143,151)
(144,152)(177,217)(178,218)(179,219)(180,220)(181,221)(182,222)(183,223)
(184,224)(185,209)(186,210)(187,211)(188,212)(189,213)(190,214)(191,215)
(192,216)(193,201)(194,202)(195,203)(196,204)(197,205)(198,206)(199,207)
(200,208)(233,273)(234,274)(235,275)(236,276)(237,277)(238,278)(239,279)
(240,280)(241,265)(242,266)(243,267)(244,268)(245,269)(246,270)(247,271)
(248,272)(249,257)(250,258)(251,259)(252,260)(253,261)(254,262)(255,263)
(256,264)(289,329)(290,330)(291,331)(292,332)(293,333)(294,334)(295,335)
(296,336)(297,321)(298,322)(299,323)(300,324)(301,325)(302,326)(303,327)
(304,328)(305,313)(306,314)(307,315)(308,316)(309,317)(310,318)(311,319)
(312,320);
s1 := Sym(336)!( 1,181)( 2,182)( 3,184)( 4,183)( 5,178)( 6,177)( 7,179)
( 8,180)( 9,173)( 10,174)( 11,176)( 12,175)( 13,170)( 14,169)( 15,171)
( 16,172)( 17,221)( 18,222)( 19,224)( 20,223)( 21,218)( 22,217)( 23,219)
( 24,220)( 25,213)( 26,214)( 27,216)( 28,215)( 29,210)( 30,209)( 31,211)
( 32,212)( 33,205)( 34,206)( 35,208)( 36,207)( 37,202)( 38,201)( 39,203)
( 40,204)( 41,197)( 42,198)( 43,200)( 44,199)( 45,194)( 46,193)( 47,195)
( 48,196)( 49,189)( 50,190)( 51,192)( 52,191)( 53,186)( 54,185)( 55,187)
( 56,188)( 57,237)( 58,238)( 59,240)( 60,239)( 61,234)( 62,233)( 63,235)
( 64,236)( 65,229)( 66,230)( 67,232)( 68,231)( 69,226)( 70,225)( 71,227)
( 72,228)( 73,277)( 74,278)( 75,280)( 76,279)( 77,274)( 78,273)( 79,275)
( 80,276)( 81,269)( 82,270)( 83,272)( 84,271)( 85,266)( 86,265)( 87,267)
( 88,268)( 89,261)( 90,262)( 91,264)( 92,263)( 93,258)( 94,257)( 95,259)
( 96,260)( 97,253)( 98,254)( 99,256)(100,255)(101,250)(102,249)(103,251)
(104,252)(105,245)(106,246)(107,248)(108,247)(109,242)(110,241)(111,243)
(112,244)(113,293)(114,294)(115,296)(116,295)(117,290)(118,289)(119,291)
(120,292)(121,285)(122,286)(123,288)(124,287)(125,282)(126,281)(127,283)
(128,284)(129,333)(130,334)(131,336)(132,335)(133,330)(134,329)(135,331)
(136,332)(137,325)(138,326)(139,328)(140,327)(141,322)(142,321)(143,323)
(144,324)(145,317)(146,318)(147,320)(148,319)(149,314)(150,313)(151,315)
(152,316)(153,309)(154,310)(155,312)(156,311)(157,306)(158,305)(159,307)
(160,308)(161,301)(162,302)(163,304)(164,303)(165,298)(166,297)(167,299)
(168,300);
s2 := Sym(336)!( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)
( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)
( 43, 44)( 45, 47)( 46, 48)( 51, 52)( 53, 55)( 54, 56)( 57,113)( 58,114)
( 59,116)( 60,115)( 61,119)( 62,120)( 63,117)( 64,118)( 65,121)( 66,122)
( 67,124)( 68,123)( 69,127)( 70,128)( 71,125)( 72,126)( 73,129)( 74,130)
( 75,132)( 76,131)( 77,135)( 78,136)( 79,133)( 80,134)( 81,137)( 82,138)
( 83,140)( 84,139)( 85,143)( 86,144)( 87,141)( 88,142)( 89,145)( 90,146)
( 91,148)( 92,147)( 93,151)( 94,152)( 95,149)( 96,150)( 97,153)( 98,154)
( 99,156)(100,155)(101,159)(102,160)(103,157)(104,158)(105,161)(106,162)
(107,164)(108,163)(109,167)(110,168)(111,165)(112,166)(169,170)(173,176)
(174,175)(177,178)(181,184)(182,183)(185,186)(189,192)(190,191)(193,194)
(197,200)(198,199)(201,202)(205,208)(206,207)(209,210)(213,216)(214,215)
(217,218)(221,224)(222,223)(225,282)(226,281)(227,283)(228,284)(229,288)
(230,287)(231,286)(232,285)(233,290)(234,289)(235,291)(236,292)(237,296)
(238,295)(239,294)(240,293)(241,298)(242,297)(243,299)(244,300)(245,304)
(246,303)(247,302)(248,301)(249,306)(250,305)(251,307)(252,308)(253,312)
(254,311)(255,310)(256,309)(257,314)(258,313)(259,315)(260,316)(261,320)
(262,319)(263,318)(264,317)(265,322)(266,321)(267,323)(268,324)(269,328)
(270,327)(271,326)(272,325)(273,330)(274,329)(275,331)(276,332)(277,336)
(278,335)(279,334)(280,333);
s3 := Sym(336)!( 1, 57)( 2, 58)( 3, 63)( 4, 64)( 5, 62)( 6, 61)( 7, 59)
( 8, 60)( 9, 65)( 10, 66)( 11, 71)( 12, 72)( 13, 70)( 14, 69)( 15, 67)
( 16, 68)( 17, 73)( 18, 74)( 19, 79)( 20, 80)( 21, 78)( 22, 77)( 23, 75)
( 24, 76)( 25, 81)( 26, 82)( 27, 87)( 28, 88)( 29, 86)( 30, 85)( 31, 83)
( 32, 84)( 33, 89)( 34, 90)( 35, 95)( 36, 96)( 37, 94)( 38, 93)( 39, 91)
( 40, 92)( 41, 97)( 42, 98)( 43,103)( 44,104)( 45,102)( 46,101)( 47, 99)
( 48,100)( 49,105)( 50,106)( 51,111)( 52,112)( 53,110)( 54,109)( 55,107)
( 56,108)(115,119)(116,120)(117,118)(123,127)(124,128)(125,126)(131,135)
(132,136)(133,134)(139,143)(140,144)(141,142)(147,151)(148,152)(149,150)
(155,159)(156,160)(157,158)(163,167)(164,168)(165,166)(169,226)(170,225)
(171,232)(172,231)(173,229)(174,230)(175,228)(176,227)(177,234)(178,233)
(179,240)(180,239)(181,237)(182,238)(183,236)(184,235)(185,242)(186,241)
(187,248)(188,247)(189,245)(190,246)(191,244)(192,243)(193,250)(194,249)
(195,256)(196,255)(197,253)(198,254)(199,252)(200,251)(201,258)(202,257)
(203,264)(204,263)(205,261)(206,262)(207,260)(208,259)(209,266)(210,265)
(211,272)(212,271)(213,269)(214,270)(215,268)(216,267)(217,274)(218,273)
(219,280)(220,279)(221,277)(222,278)(223,276)(224,275)(281,282)(283,288)
(284,287)(289,290)(291,296)(292,295)(297,298)(299,304)(300,303)(305,306)
(307,312)(308,311)(313,314)(315,320)(316,319)(321,322)(323,328)(324,327)
(329,330)(331,336)(332,335);
poly := sub<Sym(336)|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,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
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 >;
References : None.
to this polytope