Polytope of Type {2,39,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,39,4}*1248
if this polytope has a name.
Group : SmallGroup(1248,1441)
Rank : 4
Schlafli Type : {2,39,4}
Number of vertices, edges, etc : 2, 78, 156, 8
Order of s0s1s2s3 : 78
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,39,4}*624
4-fold quotients : {2,39,2}*312
12-fold quotients : {2,13,2}*104
13-fold quotients : {2,3,4}*96
26-fold quotients : {2,3,4}*48
52-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 51)( 8, 53)( 9, 52)( 10, 54)( 11, 47)( 12, 49)( 13, 48)
( 14, 50)( 15, 43)( 16, 45)( 17, 44)( 18, 46)( 19, 39)( 20, 41)( 21, 40)
( 22, 42)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 27, 31)( 28, 33)( 29, 32)
( 30, 34)( 55,107)( 56,109)( 57,108)( 58,110)( 59,155)( 60,157)( 61,156)
( 62,158)( 63,151)( 64,153)( 65,152)( 66,154)( 67,147)( 68,149)( 69,148)
( 70,150)( 71,143)( 72,145)( 73,144)( 74,146)( 75,139)( 76,141)( 77,140)
( 78,142)( 79,135)( 80,137)( 81,136)( 82,138)( 83,131)( 84,133)( 85,132)
( 86,134)( 87,127)( 88,129)( 89,128)( 90,130)( 91,123)( 92,125)( 93,124)
( 94,126)( 95,119)( 96,121)( 97,120)( 98,122)( 99,115)(100,117)(101,116)
(102,118)(103,111)(104,113)(105,112)(106,114)(160,161)(163,207)(164,209)
(165,208)(166,210)(167,203)(168,205)(169,204)(170,206)(171,199)(172,201)
(173,200)(174,202)(175,195)(176,197)(177,196)(178,198)(179,191)(180,193)
(181,192)(182,194)(183,187)(184,189)(185,188)(186,190)(211,263)(212,265)
(213,264)(214,266)(215,311)(216,313)(217,312)(218,314)(219,307)(220,309)
(221,308)(222,310)(223,303)(224,305)(225,304)(226,306)(227,299)(228,301)
(229,300)(230,302)(231,295)(232,297)(233,296)(234,298)(235,291)(236,293)
(237,292)(238,294)(239,287)(240,289)(241,288)(242,290)(243,283)(244,285)
(245,284)(246,286)(247,279)(248,281)(249,280)(250,282)(251,275)(252,277)
(253,276)(254,278)(255,271)(256,273)(257,272)(258,274)(259,267)(260,269)
(261,268)(262,270);;
s2 := ( 3, 59)( 4, 60)( 5, 62)( 6, 61)( 7, 55)( 8, 56)( 9, 58)( 10, 57)
( 11,103)( 12,104)( 13,106)( 14,105)( 15, 99)( 16,100)( 17,102)( 18,101)
( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 91)( 24, 92)( 25, 94)( 26, 93)
( 27, 87)( 28, 88)( 29, 90)( 30, 89)( 31, 83)( 32, 84)( 33, 86)( 34, 85)
( 35, 79)( 36, 80)( 37, 82)( 38, 81)( 39, 75)( 40, 76)( 41, 78)( 42, 77)
( 43, 71)( 44, 72)( 45, 74)( 46, 73)( 47, 67)( 48, 68)( 49, 70)( 50, 69)
( 51, 63)( 52, 64)( 53, 66)( 54, 65)(107,111)(108,112)(109,114)(110,113)
(115,155)(116,156)(117,158)(118,157)(119,151)(120,152)(121,154)(122,153)
(123,147)(124,148)(125,150)(126,149)(127,143)(128,144)(129,146)(130,145)
(131,139)(132,140)(133,142)(134,141)(137,138)(159,215)(160,216)(161,218)
(162,217)(163,211)(164,212)(165,214)(166,213)(167,259)(168,260)(169,262)
(170,261)(171,255)(172,256)(173,258)(174,257)(175,251)(176,252)(177,254)
(178,253)(179,247)(180,248)(181,250)(182,249)(183,243)(184,244)(185,246)
(186,245)(187,239)(188,240)(189,242)(190,241)(191,235)(192,236)(193,238)
(194,237)(195,231)(196,232)(197,234)(198,233)(199,227)(200,228)(201,230)
(202,229)(203,223)(204,224)(205,226)(206,225)(207,219)(208,220)(209,222)
(210,221)(263,267)(264,268)(265,270)(266,269)(271,311)(272,312)(273,314)
(274,313)(275,307)(276,308)(277,310)(278,309)(279,303)(280,304)(281,306)
(282,305)(283,299)(284,300)(285,302)(286,301)(287,295)(288,296)(289,298)
(290,297)(293,294);;
s3 := ( 3,162)( 4,161)( 5,160)( 6,159)( 7,166)( 8,165)( 9,164)( 10,163)
( 11,170)( 12,169)( 13,168)( 14,167)( 15,174)( 16,173)( 17,172)( 18,171)
( 19,178)( 20,177)( 21,176)( 22,175)( 23,182)( 24,181)( 25,180)( 26,179)
( 27,186)( 28,185)( 29,184)( 30,183)( 31,190)( 32,189)( 33,188)( 34,187)
( 35,194)( 36,193)( 37,192)( 38,191)( 39,198)( 40,197)( 41,196)( 42,195)
( 43,202)( 44,201)( 45,200)( 46,199)( 47,206)( 48,205)( 49,204)( 50,203)
( 51,210)( 52,209)( 53,208)( 54,207)( 55,214)( 56,213)( 57,212)( 58,211)
( 59,218)( 60,217)( 61,216)( 62,215)( 63,222)( 64,221)( 65,220)( 66,219)
( 67,226)( 68,225)( 69,224)( 70,223)( 71,230)( 72,229)( 73,228)( 74,227)
( 75,234)( 76,233)( 77,232)( 78,231)( 79,238)( 80,237)( 81,236)( 82,235)
( 83,242)( 84,241)( 85,240)( 86,239)( 87,246)( 88,245)( 89,244)( 90,243)
( 91,250)( 92,249)( 93,248)( 94,247)( 95,254)( 96,253)( 97,252)( 98,251)
( 99,258)(100,257)(101,256)(102,255)(103,262)(104,261)(105,260)(106,259)
(107,266)(108,265)(109,264)(110,263)(111,270)(112,269)(113,268)(114,267)
(115,274)(116,273)(117,272)(118,271)(119,278)(120,277)(121,276)(122,275)
(123,282)(124,281)(125,280)(126,279)(127,286)(128,285)(129,284)(130,283)
(131,290)(132,289)(133,288)(134,287)(135,294)(136,293)(137,292)(138,291)
(139,298)(140,297)(141,296)(142,295)(143,302)(144,301)(145,300)(146,299)
(147,306)(148,305)(149,304)(150,303)(151,310)(152,309)(153,308)(154,307)
(155,314)(156,313)(157,312)(158,311);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(314)!(1,2);
s1 := Sym(314)!( 4, 5)( 7, 51)( 8, 53)( 9, 52)( 10, 54)( 11, 47)( 12, 49)
( 13, 48)( 14, 50)( 15, 43)( 16, 45)( 17, 44)( 18, 46)( 19, 39)( 20, 41)
( 21, 40)( 22, 42)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 27, 31)( 28, 33)
( 29, 32)( 30, 34)( 55,107)( 56,109)( 57,108)( 58,110)( 59,155)( 60,157)
( 61,156)( 62,158)( 63,151)( 64,153)( 65,152)( 66,154)( 67,147)( 68,149)
( 69,148)( 70,150)( 71,143)( 72,145)( 73,144)( 74,146)( 75,139)( 76,141)
( 77,140)( 78,142)( 79,135)( 80,137)( 81,136)( 82,138)( 83,131)( 84,133)
( 85,132)( 86,134)( 87,127)( 88,129)( 89,128)( 90,130)( 91,123)( 92,125)
( 93,124)( 94,126)( 95,119)( 96,121)( 97,120)( 98,122)( 99,115)(100,117)
(101,116)(102,118)(103,111)(104,113)(105,112)(106,114)(160,161)(163,207)
(164,209)(165,208)(166,210)(167,203)(168,205)(169,204)(170,206)(171,199)
(172,201)(173,200)(174,202)(175,195)(176,197)(177,196)(178,198)(179,191)
(180,193)(181,192)(182,194)(183,187)(184,189)(185,188)(186,190)(211,263)
(212,265)(213,264)(214,266)(215,311)(216,313)(217,312)(218,314)(219,307)
(220,309)(221,308)(222,310)(223,303)(224,305)(225,304)(226,306)(227,299)
(228,301)(229,300)(230,302)(231,295)(232,297)(233,296)(234,298)(235,291)
(236,293)(237,292)(238,294)(239,287)(240,289)(241,288)(242,290)(243,283)
(244,285)(245,284)(246,286)(247,279)(248,281)(249,280)(250,282)(251,275)
(252,277)(253,276)(254,278)(255,271)(256,273)(257,272)(258,274)(259,267)
(260,269)(261,268)(262,270);
s2 := Sym(314)!( 3, 59)( 4, 60)( 5, 62)( 6, 61)( 7, 55)( 8, 56)( 9, 58)
( 10, 57)( 11,103)( 12,104)( 13,106)( 14,105)( 15, 99)( 16,100)( 17,102)
( 18,101)( 19, 95)( 20, 96)( 21, 98)( 22, 97)( 23, 91)( 24, 92)( 25, 94)
( 26, 93)( 27, 87)( 28, 88)( 29, 90)( 30, 89)( 31, 83)( 32, 84)( 33, 86)
( 34, 85)( 35, 79)( 36, 80)( 37, 82)( 38, 81)( 39, 75)( 40, 76)( 41, 78)
( 42, 77)( 43, 71)( 44, 72)( 45, 74)( 46, 73)( 47, 67)( 48, 68)( 49, 70)
( 50, 69)( 51, 63)( 52, 64)( 53, 66)( 54, 65)(107,111)(108,112)(109,114)
(110,113)(115,155)(116,156)(117,158)(118,157)(119,151)(120,152)(121,154)
(122,153)(123,147)(124,148)(125,150)(126,149)(127,143)(128,144)(129,146)
(130,145)(131,139)(132,140)(133,142)(134,141)(137,138)(159,215)(160,216)
(161,218)(162,217)(163,211)(164,212)(165,214)(166,213)(167,259)(168,260)
(169,262)(170,261)(171,255)(172,256)(173,258)(174,257)(175,251)(176,252)
(177,254)(178,253)(179,247)(180,248)(181,250)(182,249)(183,243)(184,244)
(185,246)(186,245)(187,239)(188,240)(189,242)(190,241)(191,235)(192,236)
(193,238)(194,237)(195,231)(196,232)(197,234)(198,233)(199,227)(200,228)
(201,230)(202,229)(203,223)(204,224)(205,226)(206,225)(207,219)(208,220)
(209,222)(210,221)(263,267)(264,268)(265,270)(266,269)(271,311)(272,312)
(273,314)(274,313)(275,307)(276,308)(277,310)(278,309)(279,303)(280,304)
(281,306)(282,305)(283,299)(284,300)(285,302)(286,301)(287,295)(288,296)
(289,298)(290,297)(293,294);
s3 := Sym(314)!( 3,162)( 4,161)( 5,160)( 6,159)( 7,166)( 8,165)( 9,164)
( 10,163)( 11,170)( 12,169)( 13,168)( 14,167)( 15,174)( 16,173)( 17,172)
( 18,171)( 19,178)( 20,177)( 21,176)( 22,175)( 23,182)( 24,181)( 25,180)
( 26,179)( 27,186)( 28,185)( 29,184)( 30,183)( 31,190)( 32,189)( 33,188)
( 34,187)( 35,194)( 36,193)( 37,192)( 38,191)( 39,198)( 40,197)( 41,196)
( 42,195)( 43,202)( 44,201)( 45,200)( 46,199)( 47,206)( 48,205)( 49,204)
( 50,203)( 51,210)( 52,209)( 53,208)( 54,207)( 55,214)( 56,213)( 57,212)
( 58,211)( 59,218)( 60,217)( 61,216)( 62,215)( 63,222)( 64,221)( 65,220)
( 66,219)( 67,226)( 68,225)( 69,224)( 70,223)( 71,230)( 72,229)( 73,228)
( 74,227)( 75,234)( 76,233)( 77,232)( 78,231)( 79,238)( 80,237)( 81,236)
( 82,235)( 83,242)( 84,241)( 85,240)( 86,239)( 87,246)( 88,245)( 89,244)
( 90,243)( 91,250)( 92,249)( 93,248)( 94,247)( 95,254)( 96,253)( 97,252)
( 98,251)( 99,258)(100,257)(101,256)(102,255)(103,262)(104,261)(105,260)
(106,259)(107,266)(108,265)(109,264)(110,263)(111,270)(112,269)(113,268)
(114,267)(115,274)(116,273)(117,272)(118,271)(119,278)(120,277)(121,276)
(122,275)(123,282)(124,281)(125,280)(126,279)(127,286)(128,285)(129,284)
(130,283)(131,290)(132,289)(133,288)(134,287)(135,294)(136,293)(137,292)
(138,291)(139,298)(140,297)(141,296)(142,295)(143,302)(144,301)(145,300)
(146,299)(147,306)(148,305)(149,304)(150,303)(151,310)(152,309)(153,308)
(154,307)(155,314)(156,313)(157,312)(158,311);
poly := sub<Sym(314)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope