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