Polytope of Type {2,5,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,8}*1280b
if this polytope has a name.
Group : SmallGroup(1280,1116454)
Rank : 4
Schlafli Type : {2,5,8}
Number of vertices, edges, etc : 2, 40, 160, 64
Order of s0s1s2s3 : 20
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 : {2,5,4}*640
4-fold quotients : {2,5,4}*320
32-fold quotients : {2,5,2}*40
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)(163,164)(165,189)(166,190)(167,178)(168,177)(169,184)(170,183)(171,179)(172,180)(175,193)(176,194)(181,182)(185,192)(186,191)(195,292)(196,291)(197,317)(198,318)(199,306)(200,305)(201,312)(202,311)(203,307)(204,308)(205,301)(206,302)(207,321)(208,322)(209,296)(210,295)(211,299)(212,300)(213,310)(214,309)(215,298)(216,297)(217,320)(218,319)(219,315)(220,316)(221,293)(222,294)(223,314)(224,313)(225,303)(226,304)(227,260)(228,259)(229,285)(230,286)(231,274)(232,273)(233,280)(234,279)(235,275)(236,276)(237,269)(238,270)(239,289)(240,290)(241,264)(242,263)(243,267)(244,268)(245,278)(246,277)(247,266)(248,265)(249,288)(250,287)(251,283)(252,284)(253,261)(254,262)(255,282)(256,281)(257,271)(258,272);;
s2 := ( 3, 35)( 4, 36)( 5, 57)( 6, 58)( 7, 59)( 8, 60)( 9, 49)( 10, 50)( 11, 44)( 12, 43)( 13, 65)( 14, 66)( 15, 52)( 16, 51)( 17, 41)( 18, 42)( 19, 48)( 20, 47)( 21, 61)( 22, 62)( 23, 56)( 24, 55)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 53)( 30, 54)( 31, 63)( 32, 64)( 33, 45)( 34, 46)( 67,131)( 68,132)( 69,153)( 70,154)( 71,155)( 72,156)( 73,145)( 74,146)( 75,140)( 76,139)( 77,161)( 78,162)( 79,148)( 80,147)( 81,137)( 82,138)( 83,144)( 84,143)( 85,157)( 86,158)( 87,152)( 88,151)( 89,133)( 90,134)( 91,135)( 92,136)( 93,149)( 94,150)( 95,159)( 96,160)( 97,141)( 98,142)(101,121)(102,122)(103,123)(104,124)(105,113)(106,114)(107,108)(109,129)(110,130)(111,116)(112,115)(117,125)(118,126)(119,120)(163,196)(164,195)(165,218)(166,217)(167,220)(168,219)(169,210)(170,209)(171,203)(172,204)(173,226)(174,225)(175,211)(176,212)(177,202)(178,201)(179,207)(180,208)(181,222)(182,221)(183,215)(184,216)(185,198)(186,197)(187,200)(188,199)(189,214)(190,213)(191,224)(192,223)(193,206)(194,205)(227,292)(228,291)(229,314)(230,313)(231,316)(232,315)(233,306)(234,305)(235,299)(236,300)(237,322)(238,321)(239,307)(240,308)(241,298)(242,297)(243,303)(244,304)(245,318)(246,317)(247,311)(248,312)(249,294)(250,293)(251,296)(252,295)(253,310)(254,309)(255,320)(256,319)(257,302)(258,301)(259,260)(261,282)(262,281)(263,284)(264,283)(265,274)(266,273)(269,290)(270,289)(271,275)(272,276)(277,286)(278,285)(287,288);;
s3 := ( 3,173)( 4,174)( 5,171)( 6,172)( 7,178)( 8,177)( 9,176)( 10,175)( 11,166)( 12,165)( 13,164)( 14,163)( 15,169)( 16,170)( 17,167)( 18,168)( 19,189)( 20,190)( 21,187)( 22,188)( 23,194)( 24,193)( 25,192)( 26,191)( 27,182)( 28,181)( 29,180)( 30,179)( 31,185)( 32,186)( 33,183)( 34,184)( 35,205)( 36,206)( 37,203)( 38,204)( 39,210)( 40,209)( 41,208)( 42,207)( 43,198)( 44,197)( 45,196)( 46,195)( 47,201)( 48,202)( 49,199)( 50,200)( 51,221)( 52,222)( 53,219)( 54,220)( 55,226)( 56,225)( 57,224)( 58,223)( 59,214)( 60,213)( 61,212)( 62,211)( 63,217)( 64,218)( 65,215)( 66,216)( 67,237)( 68,238)( 69,235)( 70,236)( 71,242)( 72,241)( 73,240)( 74,239)( 75,230)( 76,229)( 77,228)( 78,227)( 79,233)( 80,234)( 81,231)( 82,232)( 83,253)( 84,254)( 85,251)( 86,252)( 87,258)( 88,257)( 89,256)( 90,255)( 91,246)( 92,245)( 93,244)( 94,243)( 95,249)( 96,250)( 97,247)( 98,248)( 99,269)(100,270)(101,267)(102,268)(103,274)(104,273)(105,272)(106,271)(107,262)(108,261)(109,260)(110,259)(111,265)(112,266)(113,263)(114,264)(115,285)(116,286)(117,283)(118,284)(119,290)(120,289)(121,288)(122,287)(123,278)(124,277)(125,276)(126,275)(127,281)(128,282)(129,279)(130,280)(131,301)(132,302)(133,299)(134,300)(135,306)(136,305)(137,304)(138,303)(139,294)(140,293)(141,292)(142,291)(143,297)(144,298)(145,295)(146,296)(147,317)(148,318)(149,315)(150,316)(151,322)(152,321)(153,320)(154,319)(155,310)(156,309)(157,308)(158,307)(159,313)(160,314)(161,311)(162,312);;
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*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*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)(163,164)(165,189)(166,190)(167,178)(168,177)(169,184)(170,183)(171,179)(172,180)(175,193)(176,194)(181,182)(185,192)(186,191)(195,292)(196,291)(197,317)(198,318)(199,306)(200,305)(201,312)(202,311)(203,307)(204,308)(205,301)(206,302)(207,321)(208,322)(209,296)(210,295)(211,299)(212,300)(213,310)(214,309)(215,298)(216,297)(217,320)(218,319)(219,315)(220,316)(221,293)(222,294)(223,314)(224,313)(225,303)(226,304)(227,260)(228,259)(229,285)(230,286)(231,274)(232,273)(233,280)(234,279)(235,275)(236,276)(237,269)(238,270)(239,289)(240,290)(241,264)(242,263)(243,267)(244,268)(245,278)(246,277)(247,266)(248,265)(249,288)(250,287)(251,283)(252,284)(253,261)(254,262)(255,282)(256,281)(257,271)(258,272);
s2 := Sym(322)!( 3, 35)( 4, 36)( 5, 57)( 6, 58)( 7, 59)( 8, 60)( 9, 49)( 10, 50)( 11, 44)( 12, 43)( 13, 65)( 14, 66)( 15, 52)( 16, 51)( 17, 41)( 18, 42)( 19, 48)( 20, 47)( 21, 61)( 22, 62)( 23, 56)( 24, 55)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 53)( 30, 54)( 31, 63)( 32, 64)( 33, 45)( 34, 46)( 67,131)( 68,132)( 69,153)( 70,154)( 71,155)( 72,156)( 73,145)( 74,146)( 75,140)( 76,139)( 77,161)( 78,162)( 79,148)( 80,147)( 81,137)( 82,138)( 83,144)( 84,143)( 85,157)( 86,158)( 87,152)( 88,151)( 89,133)( 90,134)( 91,135)( 92,136)( 93,149)( 94,150)( 95,159)( 96,160)( 97,141)( 98,142)(101,121)(102,122)(103,123)(104,124)(105,113)(106,114)(107,108)(109,129)(110,130)(111,116)(112,115)(117,125)(118,126)(119,120)(163,196)(164,195)(165,218)(166,217)(167,220)(168,219)(169,210)(170,209)(171,203)(172,204)(173,226)(174,225)(175,211)(176,212)(177,202)(178,201)(179,207)(180,208)(181,222)(182,221)(183,215)(184,216)(185,198)(186,197)(187,200)(188,199)(189,214)(190,213)(191,224)(192,223)(193,206)(194,205)(227,292)(228,291)(229,314)(230,313)(231,316)(232,315)(233,306)(234,305)(235,299)(236,300)(237,322)(238,321)(239,307)(240,308)(241,298)(242,297)(243,303)(244,304)(245,318)(246,317)(247,311)(248,312)(249,294)(250,293)(251,296)(252,295)(253,310)(254,309)(255,320)(256,319)(257,302)(258,301)(259,260)(261,282)(262,281)(263,284)(264,283)(265,274)(266,273)(269,290)(270,289)(271,275)(272,276)(277,286)(278,285)(287,288);
s3 := Sym(322)!( 3,173)( 4,174)( 5,171)( 6,172)( 7,178)( 8,177)( 9,176)( 10,175)( 11,166)( 12,165)( 13,164)( 14,163)( 15,169)( 16,170)( 17,167)( 18,168)( 19,189)( 20,190)( 21,187)( 22,188)( 23,194)( 24,193)( 25,192)( 26,191)( 27,182)( 28,181)( 29,180)( 30,179)( 31,185)( 32,186)( 33,183)( 34,184)( 35,205)( 36,206)( 37,203)( 38,204)( 39,210)( 40,209)( 41,208)( 42,207)( 43,198)( 44,197)( 45,196)( 46,195)( 47,201)( 48,202)( 49,199)( 50,200)( 51,221)( 52,222)( 53,219)( 54,220)( 55,226)( 56,225)( 57,224)( 58,223)( 59,214)( 60,213)( 61,212)( 62,211)( 63,217)( 64,218)( 65,215)( 66,216)( 67,237)( 68,238)( 69,235)( 70,236)( 71,242)( 72,241)( 73,240)( 74,239)( 75,230)( 76,229)( 77,228)( 78,227)( 79,233)( 80,234)( 81,231)( 82,232)( 83,253)( 84,254)( 85,251)( 86,252)( 87,258)( 88,257)( 89,256)( 90,255)( 91,246)( 92,245)( 93,244)( 94,243)( 95,249)( 96,250)( 97,247)( 98,248)( 99,269)(100,270)(101,267)(102,268)(103,274)(104,273)(105,272)(106,271)(107,262)(108,261)(109,260)(110,259)(111,265)(112,266)(113,263)(114,264)(115,285)(116,286)(117,283)(118,284)(119,290)(120,289)(121,288)(122,287)(123,278)(124,277)(125,276)(126,275)(127,281)(128,282)(129,279)(130,280)(131,301)(132,302)(133,299)(134,300)(135,306)(136,305)(137,304)(138,303)(139,294)(140,293)(141,292)(142,291)(143,297)(144,298)(145,295)(146,296)(147,317)(148,318)(149,315)(150,316)(151,322)(152,321)(153,320)(154,319)(155,310)(156,309)(157,308)(158,307)(159,313)(160,314)(161,311)(162,312);
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*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2 >;
to this polytope