Polytope of Type {4,78,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,78,2}*1248c
if this polytope has a name.
Group : SmallGroup(1248,1441)
Rank : 4
Schlafli Type : {4,78,2}
Number of vertices, edges, etc : 4, 156, 78, 2
Order of s0s1s2s3 : 78
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {4,39,2}*624
   13-fold quotients : {4,6,2}*96b
   26-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.

Permutation Representation (GAP) : 
s0 := (  1,159)(  2,160)(  3,157)(  4,158)(  5,163)(  6,164)(  7,161)(  8,162)(  9,167)( 10,168)( 11,165)( 12,166)( 13,171)( 14,172)( 15,169)( 16,170)( 17,175)( 18,176)( 19,173)( 20,174)( 21,179)( 22,180)( 23,177)( 24,178)( 25,183)( 26,184)( 27,181)( 28,182)( 29,187)( 30,188)( 31,185)( 32,186)( 33,191)( 34,192)( 35,189)( 36,190)( 37,195)( 38,196)( 39,193)( 40,194)( 41,199)( 42,200)( 43,197)( 44,198)( 45,203)( 46,204)( 47,201)( 48,202)( 49,207)( 50,208)( 51,205)( 52,206)( 53,211)( 54,212)( 55,209)( 56,210)( 57,215)( 58,216)( 59,213)( 60,214)( 61,219)( 62,220)( 63,217)( 64,218)( 65,223)( 66,224)( 67,221)( 68,222)( 69,227)( 70,228)( 71,225)( 72,226)( 73,231)( 74,232)( 75,229)( 76,230)( 77,235)( 78,236)( 79,233)( 80,234)( 81,239)( 82,240)( 83,237)( 84,238)( 85,243)( 86,244)( 87,241)( 88,242)( 89,247)( 90,248)( 91,245)( 92,246)( 93,251)( 94,252)( 95,249)( 96,250)( 97,255)( 98,256)( 99,253)(100,254)(101,259)(102,260)(103,257)(104,258)(105,263)(106,264)(107,261)(108,262)(109,267)(110,268)(111,265)(112,266)(113,271)(114,272)(115,269)(116,270)(117,275)(118,276)(119,273)(120,274)(121,279)(122,280)(123,277)(124,278)(125,283)(126,284)(127,281)(128,282)(129,287)(130,288)(131,285)(132,286)(133,291)(134,292)(135,289)(136,290)(137,295)(138,296)(139,293)(140,294)(141,299)(142,300)(143,297)(144,298)(145,303)(146,304)(147,301)(148,302)(149,307)(150,308)(151,305)(152,306)(153,311)(154,312)(155,309)(156,310);;
s1 := (  2,  3)(  5, 49)(  6, 51)(  7, 50)(  8, 52)(  9, 45)( 10, 47)( 11, 46)( 12, 48)( 13, 41)( 14, 43)( 15, 42)( 16, 44)( 17, 37)( 18, 39)( 19, 38)( 20, 40)( 21, 33)( 22, 35)( 23, 34)( 24, 36)( 25, 29)( 26, 31)( 27, 30)( 28, 32)( 53,105)( 54,107)( 55,106)( 56,108)( 57,153)( 58,155)( 59,154)( 60,156)( 61,149)( 62,151)( 63,150)( 64,152)( 65,145)( 66,147)( 67,146)( 68,148)( 69,141)( 70,143)( 71,142)( 72,144)( 73,137)( 74,139)( 75,138)( 76,140)( 77,133)( 78,135)( 79,134)( 80,136)( 81,129)( 82,131)( 83,130)( 84,132)( 85,125)( 86,127)( 87,126)( 88,128)( 89,121)( 90,123)( 91,122)( 92,124)( 93,117)( 94,119)( 95,118)( 96,120)( 97,113)( 98,115)( 99,114)(100,116)(101,109)(102,111)(103,110)(104,112)(158,159)(161,205)(162,207)(163,206)(164,208)(165,201)(166,203)(167,202)(168,204)(169,197)(170,199)(171,198)(172,200)(173,193)(174,195)(175,194)(176,196)(177,189)(178,191)(179,190)(180,192)(181,185)(182,187)(183,186)(184,188)(209,261)(210,263)(211,262)(212,264)(213,309)(214,311)(215,310)(216,312)(217,305)(218,307)(219,306)(220,308)(221,301)(222,303)(223,302)(224,304)(225,297)(226,299)(227,298)(228,300)(229,293)(230,295)(231,294)(232,296)(233,289)(234,291)(235,290)(236,292)(237,285)(238,287)(239,286)(240,288)(241,281)(242,283)(243,282)(244,284)(245,277)(246,279)(247,278)(248,280)(249,273)(250,275)(251,274)(252,276)(253,269)(254,271)(255,270)(256,272)(257,265)(258,267)(259,266)(260,268);;
s2 := (  1,265)(  2,268)(  3,267)(  4,266)(  5,261)(  6,264)(  7,263)(  8,262)(  9,309)( 10,312)( 11,311)( 12,310)( 13,305)( 14,308)( 15,307)( 16,306)( 17,301)( 18,304)( 19,303)( 20,302)( 21,297)( 22,300)( 23,299)( 24,298)( 25,293)( 26,296)( 27,295)( 28,294)( 29,289)( 30,292)( 31,291)( 32,290)( 33,285)( 34,288)( 35,287)( 36,286)( 37,281)( 38,284)( 39,283)( 40,282)( 41,277)( 42,280)( 43,279)( 44,278)( 45,273)( 46,276)( 47,275)( 48,274)( 49,269)( 50,272)( 51,271)( 52,270)( 53,213)( 54,216)( 55,215)( 56,214)( 57,209)( 58,212)( 59,211)( 60,210)( 61,257)( 62,260)( 63,259)( 64,258)( 65,253)( 66,256)( 67,255)( 68,254)( 69,249)( 70,252)( 71,251)( 72,250)( 73,245)( 74,248)( 75,247)( 76,246)( 77,241)( 78,244)( 79,243)( 80,242)( 81,237)( 82,240)( 83,239)( 84,238)( 85,233)( 86,236)( 87,235)( 88,234)( 89,229)( 90,232)( 91,231)( 92,230)( 93,225)( 94,228)( 95,227)( 96,226)( 97,221)( 98,224)( 99,223)(100,222)(101,217)(102,220)(103,219)(104,218)(105,161)(106,164)(107,163)(108,162)(109,157)(110,160)(111,159)(112,158)(113,205)(114,208)(115,207)(116,206)(117,201)(118,204)(119,203)(120,202)(121,197)(122,200)(123,199)(124,198)(125,193)(126,196)(127,195)(128,194)(129,189)(130,192)(131,191)(132,190)(133,185)(134,188)(135,187)(136,186)(137,181)(138,184)(139,183)(140,182)(141,177)(142,180)(143,179)(144,178)(145,173)(146,176)(147,175)(148,174)(149,169)(150,172)(151,171)(152,170)(153,165)(154,168)(155,167)(156,166);;
s3 := (313,314);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
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*s0*s2*s1*s0*s2*s1*s0*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)!(  1,159)(  2,160)(  3,157)(  4,158)(  5,163)(  6,164)(  7,161)(  8,162)(  9,167)( 10,168)( 11,165)( 12,166)( 13,171)( 14,172)( 15,169)( 16,170)( 17,175)( 18,176)( 19,173)( 20,174)( 21,179)( 22,180)( 23,177)( 24,178)( 25,183)( 26,184)( 27,181)( 28,182)( 29,187)( 30,188)( 31,185)( 32,186)( 33,191)( 34,192)( 35,189)( 36,190)( 37,195)( 38,196)( 39,193)( 40,194)( 41,199)( 42,200)( 43,197)( 44,198)( 45,203)( 46,204)( 47,201)( 48,202)( 49,207)( 50,208)( 51,205)( 52,206)( 53,211)( 54,212)( 55,209)( 56,210)( 57,215)( 58,216)( 59,213)( 60,214)( 61,219)( 62,220)( 63,217)( 64,218)( 65,223)( 66,224)( 67,221)( 68,222)( 69,227)( 70,228)( 71,225)( 72,226)( 73,231)( 74,232)( 75,229)( 76,230)( 77,235)( 78,236)( 79,233)( 80,234)( 81,239)( 82,240)( 83,237)( 84,238)( 85,243)( 86,244)( 87,241)( 88,242)( 89,247)( 90,248)( 91,245)( 92,246)( 93,251)( 94,252)( 95,249)( 96,250)( 97,255)( 98,256)( 99,253)(100,254)(101,259)(102,260)(103,257)(104,258)(105,263)(106,264)(107,261)(108,262)(109,267)(110,268)(111,265)(112,266)(113,271)(114,272)(115,269)(116,270)(117,275)(118,276)(119,273)(120,274)(121,279)(122,280)(123,277)(124,278)(125,283)(126,284)(127,281)(128,282)(129,287)(130,288)(131,285)(132,286)(133,291)(134,292)(135,289)(136,290)(137,295)(138,296)(139,293)(140,294)(141,299)(142,300)(143,297)(144,298)(145,303)(146,304)(147,301)(148,302)(149,307)(150,308)(151,305)(152,306)(153,311)(154,312)(155,309)(156,310);
s1 := Sym(314)!(  2,  3)(  5, 49)(  6, 51)(  7, 50)(  8, 52)(  9, 45)( 10, 47)( 11, 46)( 12, 48)( 13, 41)( 14, 43)( 15, 42)( 16, 44)( 17, 37)( 18, 39)( 19, 38)( 20, 40)( 21, 33)( 22, 35)( 23, 34)( 24, 36)( 25, 29)( 26, 31)( 27, 30)( 28, 32)( 53,105)( 54,107)( 55,106)( 56,108)( 57,153)( 58,155)( 59,154)( 60,156)( 61,149)( 62,151)( 63,150)( 64,152)( 65,145)( 66,147)( 67,146)( 68,148)( 69,141)( 70,143)( 71,142)( 72,144)( 73,137)( 74,139)( 75,138)( 76,140)( 77,133)( 78,135)( 79,134)( 80,136)( 81,129)( 82,131)( 83,130)( 84,132)( 85,125)( 86,127)( 87,126)( 88,128)( 89,121)( 90,123)( 91,122)( 92,124)( 93,117)( 94,119)( 95,118)( 96,120)( 97,113)( 98,115)( 99,114)(100,116)(101,109)(102,111)(103,110)(104,112)(158,159)(161,205)(162,207)(163,206)(164,208)(165,201)(166,203)(167,202)(168,204)(169,197)(170,199)(171,198)(172,200)(173,193)(174,195)(175,194)(176,196)(177,189)(178,191)(179,190)(180,192)(181,185)(182,187)(183,186)(184,188)(209,261)(210,263)(211,262)(212,264)(213,309)(214,311)(215,310)(216,312)(217,305)(218,307)(219,306)(220,308)(221,301)(222,303)(223,302)(224,304)(225,297)(226,299)(227,298)(228,300)(229,293)(230,295)(231,294)(232,296)(233,289)(234,291)(235,290)(236,292)(237,285)(238,287)(239,286)(240,288)(241,281)(242,283)(243,282)(244,284)(245,277)(246,279)(247,278)(248,280)(249,273)(250,275)(251,274)(252,276)(253,269)(254,271)(255,270)(256,272)(257,265)(258,267)(259,266)(260,268);
s2 := Sym(314)!(  1,265)(  2,268)(  3,267)(  4,266)(  5,261)(  6,264)(  7,263)(  8,262)(  9,309)( 10,312)( 11,311)( 12,310)( 13,305)( 14,308)( 15,307)( 16,306)( 17,301)( 18,304)( 19,303)( 20,302)( 21,297)( 22,300)( 23,299)( 24,298)( 25,293)( 26,296)( 27,295)( 28,294)( 29,289)( 30,292)( 31,291)( 32,290)( 33,285)( 34,288)( 35,287)( 36,286)( 37,281)( 38,284)( 39,283)( 40,282)( 41,277)( 42,280)( 43,279)( 44,278)( 45,273)( 46,276)( 47,275)( 48,274)( 49,269)( 50,272)( 51,271)( 52,270)( 53,213)( 54,216)( 55,215)( 56,214)( 57,209)( 58,212)( 59,211)( 60,210)( 61,257)( 62,260)( 63,259)( 64,258)( 65,253)( 66,256)( 67,255)( 68,254)( 69,249)( 70,252)( 71,251)( 72,250)( 73,245)( 74,248)( 75,247)( 76,246)( 77,241)( 78,244)( 79,243)( 80,242)( 81,237)( 82,240)( 83,239)( 84,238)( 85,233)( 86,236)( 87,235)( 88,234)( 89,229)( 90,232)( 91,231)( 92,230)( 93,225)( 94,228)( 95,227)( 96,226)( 97,221)( 98,224)( 99,223)(100,222)(101,217)(102,220)(103,219)(104,218)(105,161)(106,164)(107,163)(108,162)(109,157)(110,160)(111,159)(112,158)(113,205)(114,208)(115,207)(116,206)(117,201)(118,204)(119,203)(120,202)(121,197)(122,200)(123,199)(124,198)(125,193)(126,196)(127,195)(128,194)(129,189)(130,192)(131,191)(132,190)(133,185)(134,188)(135,187)(136,186)(137,181)(138,184)(139,183)(140,182)(141,177)(142,180)(143,179)(144,178)(145,173)(146,176)(147,175)(148,174)(149,169)(150,172)(151,171)(152,170)(153,165)(154,168)(155,167)(156,166);
s3 := Sym(314)!(313,314);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
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*s0*s2*s1*s0*s2*s1*s0*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