Polytope of Type {2,10,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,8}*1280b
if this polytope has a name.
Group : SmallGroup(1280,1116450)
Rank : 4
Schlafli Type : {2,10,8}
Number of vertices, edges, etc : 2, 40, 160, 32
Order of s0s1s2s3 : 10
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 : {2,5,8}*640a, {2,10,4}*640a
4-fold quotients : {2,5,4}*320
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 30)( 6, 29)( 7, 17)( 8, 18)( 9, 23)( 10, 24)( 11, 20)( 12, 19)( 13, 14)( 15, 34)( 16, 33)( 25, 31)( 26, 32)( 27, 28)( 35,131)( 36,132)( 37,158)( 38,157)( 39,145)( 40,146)( 41,151)( 42,152)( 43,148)( 44,147)( 45,142)( 46,141)( 47,162)( 48,161)( 49,135)( 50,136)( 51,140)( 52,139)( 53,149)( 54,150)( 55,137)( 56,138)( 57,159)( 58,160)( 59,156)( 60,155)( 61,134)( 62,133)( 63,153)( 64,154)( 65,144)( 66,143)( 67, 99)( 68,100)( 69,126)( 70,125)( 71,113)( 72,114)( 73,119)( 74,120)( 75,116)( 76,115)( 77,110)( 78,109)( 79,130)( 80,129)( 81,103)( 82,104)( 83,108)( 84,107)( 85,117)( 86,118)( 87,105)( 88,106)( 89,127)( 90,128)( 91,124)( 92,123)( 93,102)( 94,101)( 95,121)( 96,122)( 97,112)( 98,111)(165,190)(166,189)(167,177)(168,178)(169,183)(170,184)(171,180)(172,179)(173,174)(175,194)(176,193)(185,191)(186,192)(187,188)(195,291)(196,292)(197,318)(198,317)(199,305)(200,306)(201,311)(202,312)(203,308)(204,307)(205,302)(206,301)(207,322)(208,321)(209,295)(210,296)(211,300)(212,299)(213,309)(214,310)(215,297)(216,298)(217,319)(218,320)(219,316)(220,315)(221,294)(222,293)(223,313)(224,314)(225,304)(226,303)(227,259)(228,260)(229,286)(230,285)(231,273)(232,274)(233,279)(234,280)(235,276)(236,275)(237,270)(238,269)(239,290)(240,289)(241,263)(242,264)(243,268)(244,267)(245,277)(246,278)(247,265)(248,266)(249,287)(250,288)(251,284)(252,283)(253,262)(254,261)(255,281)(256,282)(257,272)(258,271);;
s2 := ( 3,195)( 4,196)( 5,217)( 6,218)( 7,219)( 8,220)( 9,209)( 10,210)( 11,204)( 12,203)( 13,225)( 14,226)( 15,212)( 16,211)( 17,201)( 18,202)( 19,208)( 20,207)( 21,221)( 22,222)( 23,216)( 24,215)( 25,197)( 26,198)( 27,199)( 28,200)( 29,213)( 30,214)( 31,223)( 32,224)( 33,205)( 34,206)( 35,163)( 36,164)( 37,185)( 38,186)( 39,187)( 40,188)( 41,177)( 42,178)( 43,172)( 44,171)( 45,193)( 46,194)( 47,180)( 48,179)( 49,169)( 50,170)( 51,176)( 52,175)( 53,189)( 54,190)( 55,184)( 56,183)( 57,165)( 58,166)( 59,167)( 60,168)( 61,181)( 62,182)( 63,191)( 64,192)( 65,173)( 66,174)( 67,291)( 68,292)( 69,313)( 70,314)( 71,315)( 72,316)( 73,305)( 74,306)( 75,300)( 76,299)( 77,321)( 78,322)( 79,308)( 80,307)( 81,297)( 82,298)( 83,304)( 84,303)( 85,317)( 86,318)( 87,312)( 88,311)( 89,293)( 90,294)( 91,295)( 92,296)( 93,309)( 94,310)( 95,319)( 96,320)( 97,301)( 98,302)( 99,259)(100,260)(101,281)(102,282)(103,283)(104,284)(105,273)(106,274)(107,268)(108,267)(109,289)(110,290)(111,276)(112,275)(113,265)(114,266)(115,272)(116,271)(117,285)(118,286)(119,280)(120,279)(121,261)(122,262)(123,263)(124,264)(125,277)(126,278)(127,287)(128,288)(129,269)(130,270)(131,227)(132,228)(133,249)(134,250)(135,251)(136,252)(137,241)(138,242)(139,236)(140,235)(141,257)(142,258)(143,244)(144,243)(145,233)(146,234)(147,240)(148,239)(149,253)(150,254)(151,248)(152,247)(153,229)(154,230)(155,231)(156,232)(157,245)(158,246)(159,255)(160,256)(161,237)(162,238);;
s3 := ( 3, 22)( 4, 21)( 5, 19)( 6, 20)( 7, 25)( 8, 26)( 9, 24)( 10, 23)( 11, 29)( 12, 30)( 13, 28)( 14, 27)( 15, 34)( 16, 33)( 17, 31)( 18, 32)( 35, 54)( 36, 53)( 37, 51)( 38, 52)( 39, 57)( 40, 58)( 41, 56)( 42, 55)( 43, 61)( 44, 62)( 45, 60)( 46, 59)( 47, 66)( 48, 65)( 49, 63)( 50, 64)( 67, 86)( 68, 85)( 69, 83)( 70, 84)( 71, 89)( 72, 90)( 73, 88)( 74, 87)( 75, 93)( 76, 94)( 77, 92)( 78, 91)( 79, 98)( 80, 97)( 81, 95)( 82, 96)( 99,118)(100,117)(101,115)(102,116)(103,121)(104,122)(105,120)(106,119)(107,125)(108,126)(109,124)(110,123)(111,130)(112,129)(113,127)(114,128)(131,150)(132,149)(133,147)(134,148)(135,153)(136,154)(137,152)(138,151)(139,157)(140,158)(141,156)(142,155)(143,162)(144,161)(145,159)(146,160)(163,182)(164,181)(165,179)(166,180)(167,185)(168,186)(169,184)(170,183)(171,189)(172,190)(173,188)(174,187)(175,194)(176,193)(177,191)(178,192)(195,214)(196,213)(197,211)(198,212)(199,217)(200,218)(201,216)(202,215)(203,221)(204,222)(205,220)(206,219)(207,226)(208,225)(209,223)(210,224)(227,246)(228,245)(229,243)(230,244)(231,249)(232,250)(233,248)(234,247)(235,253)(236,254)(237,252)(238,251)(239,258)(240,257)(241,255)(242,256)(259,278)(260,277)(261,275)(262,276)(263,281)(264,282)(265,280)(266,279)(267,285)(268,286)(269,284)(270,283)(271,290)(272,289)(273,287)(274,288)(291,310)(292,309)(293,307)(294,308)(295,313)(296,314)(297,312)(298,311)(299,317)(300,318)(301,316)(302,315)(303,322)(304,321)(305,319)(306,320);;
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,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3*s2*s3,
s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s3*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(322)!(1,2);
s1 := Sym(322)!( 5, 30)( 6, 29)( 7, 17)( 8, 18)( 9, 23)( 10, 24)( 11, 20)( 12, 19)( 13, 14)( 15, 34)( 16, 33)( 25, 31)( 26, 32)( 27, 28)( 35,131)( 36,132)( 37,158)( 38,157)( 39,145)( 40,146)( 41,151)( 42,152)( 43,148)( 44,147)( 45,142)( 46,141)( 47,162)( 48,161)( 49,135)( 50,136)( 51,140)( 52,139)( 53,149)( 54,150)( 55,137)( 56,138)( 57,159)( 58,160)( 59,156)( 60,155)( 61,134)( 62,133)( 63,153)( 64,154)( 65,144)( 66,143)( 67, 99)( 68,100)( 69,126)( 70,125)( 71,113)( 72,114)( 73,119)( 74,120)( 75,116)( 76,115)( 77,110)( 78,109)( 79,130)( 80,129)( 81,103)( 82,104)( 83,108)( 84,107)( 85,117)( 86,118)( 87,105)( 88,106)( 89,127)( 90,128)( 91,124)( 92,123)( 93,102)( 94,101)( 95,121)( 96,122)( 97,112)( 98,111)(165,190)(166,189)(167,177)(168,178)(169,183)(170,184)(171,180)(172,179)(173,174)(175,194)(176,193)(185,191)(186,192)(187,188)(195,291)(196,292)(197,318)(198,317)(199,305)(200,306)(201,311)(202,312)(203,308)(204,307)(205,302)(206,301)(207,322)(208,321)(209,295)(210,296)(211,300)(212,299)(213,309)(214,310)(215,297)(216,298)(217,319)(218,320)(219,316)(220,315)(221,294)(222,293)(223,313)(224,314)(225,304)(226,303)(227,259)(228,260)(229,286)(230,285)(231,273)(232,274)(233,279)(234,280)(235,276)(236,275)(237,270)(238,269)(239,290)(240,289)(241,263)(242,264)(243,268)(244,267)(245,277)(246,278)(247,265)(248,266)(249,287)(250,288)(251,284)(252,283)(253,262)(254,261)(255,281)(256,282)(257,272)(258,271);
s2 := Sym(322)!( 3,195)( 4,196)( 5,217)( 6,218)( 7,219)( 8,220)( 9,209)( 10,210)( 11,204)( 12,203)( 13,225)( 14,226)( 15,212)( 16,211)( 17,201)( 18,202)( 19,208)( 20,207)( 21,221)( 22,222)( 23,216)( 24,215)( 25,197)( 26,198)( 27,199)( 28,200)( 29,213)( 30,214)( 31,223)( 32,224)( 33,205)( 34,206)( 35,163)( 36,164)( 37,185)( 38,186)( 39,187)( 40,188)( 41,177)( 42,178)( 43,172)( 44,171)( 45,193)( 46,194)( 47,180)( 48,179)( 49,169)( 50,170)( 51,176)( 52,175)( 53,189)( 54,190)( 55,184)( 56,183)( 57,165)( 58,166)( 59,167)( 60,168)( 61,181)( 62,182)( 63,191)( 64,192)( 65,173)( 66,174)( 67,291)( 68,292)( 69,313)( 70,314)( 71,315)( 72,316)( 73,305)( 74,306)( 75,300)( 76,299)( 77,321)( 78,322)( 79,308)( 80,307)( 81,297)( 82,298)( 83,304)( 84,303)( 85,317)( 86,318)( 87,312)( 88,311)( 89,293)( 90,294)( 91,295)( 92,296)( 93,309)( 94,310)( 95,319)( 96,320)( 97,301)( 98,302)( 99,259)(100,260)(101,281)(102,282)(103,283)(104,284)(105,273)(106,274)(107,268)(108,267)(109,289)(110,290)(111,276)(112,275)(113,265)(114,266)(115,272)(116,271)(117,285)(118,286)(119,280)(120,279)(121,261)(122,262)(123,263)(124,264)(125,277)(126,278)(127,287)(128,288)(129,269)(130,270)(131,227)(132,228)(133,249)(134,250)(135,251)(136,252)(137,241)(138,242)(139,236)(140,235)(141,257)(142,258)(143,244)(144,243)(145,233)(146,234)(147,240)(148,239)(149,253)(150,254)(151,248)(152,247)(153,229)(154,230)(155,231)(156,232)(157,245)(158,246)(159,255)(160,256)(161,237)(162,238);
s3 := Sym(322)!( 3, 22)( 4, 21)( 5, 19)( 6, 20)( 7, 25)( 8, 26)( 9, 24)( 10, 23)( 11, 29)( 12, 30)( 13, 28)( 14, 27)( 15, 34)( 16, 33)( 17, 31)( 18, 32)( 35, 54)( 36, 53)( 37, 51)( 38, 52)( 39, 57)( 40, 58)( 41, 56)( 42, 55)( 43, 61)( 44, 62)( 45, 60)( 46, 59)( 47, 66)( 48, 65)( 49, 63)( 50, 64)( 67, 86)( 68, 85)( 69, 83)( 70, 84)( 71, 89)( 72, 90)( 73, 88)( 74, 87)( 75, 93)( 76, 94)( 77, 92)( 78, 91)( 79, 98)( 80, 97)( 81, 95)( 82, 96)( 99,118)(100,117)(101,115)(102,116)(103,121)(104,122)(105,120)(106,119)(107,125)(108,126)(109,124)(110,123)(111,130)(112,129)(113,127)(114,128)(131,150)(132,149)(133,147)(134,148)(135,153)(136,154)(137,152)(138,151)(139,157)(140,158)(141,156)(142,155)(143,162)(144,161)(145,159)(146,160)(163,182)(164,181)(165,179)(166,180)(167,185)(168,186)(169,184)(170,183)(171,189)(172,190)(173,188)(174,187)(175,194)(176,193)(177,191)(178,192)(195,214)(196,213)(197,211)(198,212)(199,217)(200,218)(201,216)(202,215)(203,221)(204,222)(205,220)(206,219)(207,226)(208,225)(209,223)(210,224)(227,246)(228,245)(229,243)(230,244)(231,249)(232,250)(233,248)(234,247)(235,253)(236,254)(237,252)(238,251)(239,258)(240,257)(241,255)(242,256)(259,278)(260,277)(261,275)(262,276)(263,281)(264,282)(265,280)(266,279)(267,285)(268,286)(269,284)(270,283)(271,290)(272,289)(273,287)(274,288)(291,310)(292,309)(293,307)(294,308)(295,313)(296,314)(297,312)(298,311)(299,317)(300,318)(301,316)(302,315)(303,322)(304,321)(305,319)(306,320);
poly := sub<Sym(322)|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, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s3*s2*s3,
s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope