Polytope of Type {14,12,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,12,3}*1344
if this polytope has a name.
Group : SmallGroup(1344,11355)
Rank : 4
Schlafli Type : {14,12,3}
Number of vertices, edges, etc : 14, 112, 24, 4
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 : {14,6,3}*672
7-fold quotients : {2,12,3}*192
14-fold quotients : {2,6,3}*96
28-fold quotients : {2,3,3}*48
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, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)( 8, 14)
( 17, 49)( 18, 50)( 19, 52)( 20, 51)( 21, 55)( 22, 56)( 23, 53)( 24, 54)
( 25, 41)( 26, 42)( 27, 44)( 28, 43)( 29, 47)( 30, 48)( 31, 45)( 32, 46)
( 35, 36)( 37, 39)( 38, 40)( 57,121)( 58,122)( 59,124)( 60,123)( 61,127)
( 62,128)( 63,125)( 64,126)( 65,113)( 66,114)( 67,116)( 68,115)( 69,119)
( 70,120)( 71,117)( 72,118)( 73,161)( 74,162)( 75,164)( 76,163)( 77,167)
( 78,168)( 79,165)( 80,166)( 81,153)( 82,154)( 83,156)( 84,155)( 85,159)
( 86,160)( 87,157)( 88,158)( 89,145)( 90,146)( 91,148)( 92,147)( 93,151)
( 94,152)( 95,149)( 96,150)( 97,137)( 98,138)( 99,140)(100,139)(101,143)
(102,144)(103,141)(104,142)(105,129)(106,130)(107,132)(108,131)(109,135)
(110,136)(111,133)(112,134)(169,178)(170,177)(171,179)(172,180)(173,184)
(174,183)(175,182)(176,181)(185,218)(186,217)(187,219)(188,220)(189,224)
(190,223)(191,222)(192,221)(193,210)(194,209)(195,211)(196,212)(197,216)
(198,215)(199,214)(200,213)(201,202)(205,208)(206,207)(225,290)(226,289)
(227,291)(228,292)(229,296)(230,295)(231,294)(232,293)(233,282)(234,281)
(235,283)(236,284)(237,288)(238,287)(239,286)(240,285)(241,330)(242,329)
(243,331)(244,332)(245,336)(246,335)(247,334)(248,333)(249,322)(250,321)
(251,323)(252,324)(253,328)(254,327)(255,326)(256,325)(257,314)(258,313)
(259,315)(260,316)(261,320)(262,319)(263,318)(264,317)(265,306)(266,305)
(267,307)(268,308)(269,312)(270,311)(271,310)(272,309)(273,298)(274,297)
(275,299)(276,300)(277,304)(278,303)(279,302)(280,301);;
s2 := ( 1,225)( 2,226)( 3,231)( 4,232)( 5,230)( 6,229)( 7,227)( 8,228)
( 9,233)( 10,234)( 11,239)( 12,240)( 13,238)( 14,237)( 15,235)( 16,236)
( 17,241)( 18,242)( 19,247)( 20,248)( 21,246)( 22,245)( 23,243)( 24,244)
( 25,249)( 26,250)( 27,255)( 28,256)( 29,254)( 30,253)( 31,251)( 32,252)
( 33,257)( 34,258)( 35,263)( 36,264)( 37,262)( 38,261)( 39,259)( 40,260)
( 41,265)( 42,266)( 43,271)( 44,272)( 45,270)( 46,269)( 47,267)( 48,268)
( 49,273)( 50,274)( 51,279)( 52,280)( 53,278)( 54,277)( 55,275)( 56,276)
( 57,169)( 58,170)( 59,175)( 60,176)( 61,174)( 62,173)( 63,171)( 64,172)
( 65,177)( 66,178)( 67,183)( 68,184)( 69,182)( 70,181)( 71,179)( 72,180)
( 73,185)( 74,186)( 75,191)( 76,192)( 77,190)( 78,189)( 79,187)( 80,188)
( 81,193)( 82,194)( 83,199)( 84,200)( 85,198)( 86,197)( 87,195)( 88,196)
( 89,201)( 90,202)( 91,207)( 92,208)( 93,206)( 94,205)( 95,203)( 96,204)
( 97,209)( 98,210)( 99,215)(100,216)(101,214)(102,213)(103,211)(104,212)
(105,217)(106,218)(107,223)(108,224)(109,222)(110,221)(111,219)(112,220)
(113,281)(114,282)(115,287)(116,288)(117,286)(118,285)(119,283)(120,284)
(121,289)(122,290)(123,295)(124,296)(125,294)(126,293)(127,291)(128,292)
(129,297)(130,298)(131,303)(132,304)(133,302)(134,301)(135,299)(136,300)
(137,305)(138,306)(139,311)(140,312)(141,310)(142,309)(143,307)(144,308)
(145,313)(146,314)(147,319)(148,320)(149,318)(150,317)(151,315)(152,316)
(153,321)(154,322)(155,327)(156,328)(157,326)(158,325)(159,323)(160,324)
(161,329)(162,330)(163,335)(164,336)(165,334)(166,333)(167,331)(168,332);;
s3 := ( 1,171)( 2,172)( 3,169)( 4,170)( 5,174)( 6,173)( 7,175)( 8,176)
( 9,179)( 10,180)( 11,177)( 12,178)( 13,182)( 14,181)( 15,183)( 16,184)
( 17,187)( 18,188)( 19,185)( 20,186)( 21,190)( 22,189)( 23,191)( 24,192)
( 25,195)( 26,196)( 27,193)( 28,194)( 29,198)( 30,197)( 31,199)( 32,200)
( 33,203)( 34,204)( 35,201)( 36,202)( 37,206)( 38,205)( 39,207)( 40,208)
( 41,211)( 42,212)( 43,209)( 44,210)( 45,214)( 46,213)( 47,215)( 48,216)
( 49,219)( 50,220)( 51,217)( 52,218)( 53,222)( 54,221)( 55,223)( 56,224)
( 57,283)( 58,284)( 59,281)( 60,282)( 61,286)( 62,285)( 63,287)( 64,288)
( 65,291)( 66,292)( 67,289)( 68,290)( 69,294)( 70,293)( 71,295)( 72,296)
( 73,299)( 74,300)( 75,297)( 76,298)( 77,302)( 78,301)( 79,303)( 80,304)
( 81,307)( 82,308)( 83,305)( 84,306)( 85,310)( 86,309)( 87,311)( 88,312)
( 89,315)( 90,316)( 91,313)( 92,314)( 93,318)( 94,317)( 95,319)( 96,320)
( 97,323)( 98,324)( 99,321)(100,322)(101,326)(102,325)(103,327)(104,328)
(105,331)(106,332)(107,329)(108,330)(109,334)(110,333)(111,335)(112,336)
(113,227)(114,228)(115,225)(116,226)(117,230)(118,229)(119,231)(120,232)
(121,235)(122,236)(123,233)(124,234)(125,238)(126,237)(127,239)(128,240)
(129,243)(130,244)(131,241)(132,242)(133,246)(134,245)(135,247)(136,248)
(137,251)(138,252)(139,249)(140,250)(141,254)(142,253)(143,255)(144,256)
(145,259)(146,260)(147,257)(148,258)(149,262)(150,261)(151,263)(152,264)
(153,267)(154,268)(155,265)(156,266)(157,270)(158,269)(159,271)(160,272)
(161,275)(162,276)(163,273)(164,274)(165,278)(166,277)(167,279)(168,280);;
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, s3*s1*s2*s1*s2*s1*s2*s3*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, 9)( 2, 10)( 3, 12)( 4, 11)( 5, 15)( 6, 16)( 7, 13)
( 8, 14)( 17, 49)( 18, 50)( 19, 52)( 20, 51)( 21, 55)( 22, 56)( 23, 53)
( 24, 54)( 25, 41)( 26, 42)( 27, 44)( 28, 43)( 29, 47)( 30, 48)( 31, 45)
( 32, 46)( 35, 36)( 37, 39)( 38, 40)( 57,121)( 58,122)( 59,124)( 60,123)
( 61,127)( 62,128)( 63,125)( 64,126)( 65,113)( 66,114)( 67,116)( 68,115)
( 69,119)( 70,120)( 71,117)( 72,118)( 73,161)( 74,162)( 75,164)( 76,163)
( 77,167)( 78,168)( 79,165)( 80,166)( 81,153)( 82,154)( 83,156)( 84,155)
( 85,159)( 86,160)( 87,157)( 88,158)( 89,145)( 90,146)( 91,148)( 92,147)
( 93,151)( 94,152)( 95,149)( 96,150)( 97,137)( 98,138)( 99,140)(100,139)
(101,143)(102,144)(103,141)(104,142)(105,129)(106,130)(107,132)(108,131)
(109,135)(110,136)(111,133)(112,134)(169,178)(170,177)(171,179)(172,180)
(173,184)(174,183)(175,182)(176,181)(185,218)(186,217)(187,219)(188,220)
(189,224)(190,223)(191,222)(192,221)(193,210)(194,209)(195,211)(196,212)
(197,216)(198,215)(199,214)(200,213)(201,202)(205,208)(206,207)(225,290)
(226,289)(227,291)(228,292)(229,296)(230,295)(231,294)(232,293)(233,282)
(234,281)(235,283)(236,284)(237,288)(238,287)(239,286)(240,285)(241,330)
(242,329)(243,331)(244,332)(245,336)(246,335)(247,334)(248,333)(249,322)
(250,321)(251,323)(252,324)(253,328)(254,327)(255,326)(256,325)(257,314)
(258,313)(259,315)(260,316)(261,320)(262,319)(263,318)(264,317)(265,306)
(266,305)(267,307)(268,308)(269,312)(270,311)(271,310)(272,309)(273,298)
(274,297)(275,299)(276,300)(277,304)(278,303)(279,302)(280,301);
s2 := Sym(336)!( 1,225)( 2,226)( 3,231)( 4,232)( 5,230)( 6,229)( 7,227)
( 8,228)( 9,233)( 10,234)( 11,239)( 12,240)( 13,238)( 14,237)( 15,235)
( 16,236)( 17,241)( 18,242)( 19,247)( 20,248)( 21,246)( 22,245)( 23,243)
( 24,244)( 25,249)( 26,250)( 27,255)( 28,256)( 29,254)( 30,253)( 31,251)
( 32,252)( 33,257)( 34,258)( 35,263)( 36,264)( 37,262)( 38,261)( 39,259)
( 40,260)( 41,265)( 42,266)( 43,271)( 44,272)( 45,270)( 46,269)( 47,267)
( 48,268)( 49,273)( 50,274)( 51,279)( 52,280)( 53,278)( 54,277)( 55,275)
( 56,276)( 57,169)( 58,170)( 59,175)( 60,176)( 61,174)( 62,173)( 63,171)
( 64,172)( 65,177)( 66,178)( 67,183)( 68,184)( 69,182)( 70,181)( 71,179)
( 72,180)( 73,185)( 74,186)( 75,191)( 76,192)( 77,190)( 78,189)( 79,187)
( 80,188)( 81,193)( 82,194)( 83,199)( 84,200)( 85,198)( 86,197)( 87,195)
( 88,196)( 89,201)( 90,202)( 91,207)( 92,208)( 93,206)( 94,205)( 95,203)
( 96,204)( 97,209)( 98,210)( 99,215)(100,216)(101,214)(102,213)(103,211)
(104,212)(105,217)(106,218)(107,223)(108,224)(109,222)(110,221)(111,219)
(112,220)(113,281)(114,282)(115,287)(116,288)(117,286)(118,285)(119,283)
(120,284)(121,289)(122,290)(123,295)(124,296)(125,294)(126,293)(127,291)
(128,292)(129,297)(130,298)(131,303)(132,304)(133,302)(134,301)(135,299)
(136,300)(137,305)(138,306)(139,311)(140,312)(141,310)(142,309)(143,307)
(144,308)(145,313)(146,314)(147,319)(148,320)(149,318)(150,317)(151,315)
(152,316)(153,321)(154,322)(155,327)(156,328)(157,326)(158,325)(159,323)
(160,324)(161,329)(162,330)(163,335)(164,336)(165,334)(166,333)(167,331)
(168,332);
s3 := Sym(336)!( 1,171)( 2,172)( 3,169)( 4,170)( 5,174)( 6,173)( 7,175)
( 8,176)( 9,179)( 10,180)( 11,177)( 12,178)( 13,182)( 14,181)( 15,183)
( 16,184)( 17,187)( 18,188)( 19,185)( 20,186)( 21,190)( 22,189)( 23,191)
( 24,192)( 25,195)( 26,196)( 27,193)( 28,194)( 29,198)( 30,197)( 31,199)
( 32,200)( 33,203)( 34,204)( 35,201)( 36,202)( 37,206)( 38,205)( 39,207)
( 40,208)( 41,211)( 42,212)( 43,209)( 44,210)( 45,214)( 46,213)( 47,215)
( 48,216)( 49,219)( 50,220)( 51,217)( 52,218)( 53,222)( 54,221)( 55,223)
( 56,224)( 57,283)( 58,284)( 59,281)( 60,282)( 61,286)( 62,285)( 63,287)
( 64,288)( 65,291)( 66,292)( 67,289)( 68,290)( 69,294)( 70,293)( 71,295)
( 72,296)( 73,299)( 74,300)( 75,297)( 76,298)( 77,302)( 78,301)( 79,303)
( 80,304)( 81,307)( 82,308)( 83,305)( 84,306)( 85,310)( 86,309)( 87,311)
( 88,312)( 89,315)( 90,316)( 91,313)( 92,314)( 93,318)( 94,317)( 95,319)
( 96,320)( 97,323)( 98,324)( 99,321)(100,322)(101,326)(102,325)(103,327)
(104,328)(105,331)(106,332)(107,329)(108,330)(109,334)(110,333)(111,335)
(112,336)(113,227)(114,228)(115,225)(116,226)(117,230)(118,229)(119,231)
(120,232)(121,235)(122,236)(123,233)(124,234)(125,238)(126,237)(127,239)
(128,240)(129,243)(130,244)(131,241)(132,242)(133,246)(134,245)(135,247)
(136,248)(137,251)(138,252)(139,249)(140,250)(141,254)(142,253)(143,255)
(144,256)(145,259)(146,260)(147,257)(148,258)(149,262)(150,261)(151,263)
(152,264)(153,267)(154,268)(155,265)(156,266)(157,270)(158,269)(159,271)
(160,272)(161,275)(162,276)(163,273)(164,274)(165,278)(166,277)(167,279)
(168,280);
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,
s3*s1*s2*s1*s2*s1*s2*s3*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