Polytope of Type {2,10,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,5}*1280
if this polytope has a name.
Group : SmallGroup(1280,1116450)
Rank : 4
Schlafli Type : {2,10,5}
Number of vertices, edges, etc : 2, 64, 160, 32
Order of s0s1s2s3 : 8
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 : {2,5,5}*640, {2,10,5}*640a, {2,10,5}*640b
4-fold quotients : {2,5,5}*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 := ( 3,182)( 4,181)( 5,172)( 6,171)( 7,191)( 8,192)( 9,170)( 10,169)
( 11,166)( 12,165)( 13,187)( 14,188)( 15,175)( 16,176)( 17,185)( 18,186)
( 19,190)( 20,189)( 21,164)( 22,163)( 23,184)( 24,183)( 25,177)( 26,178)
( 27,173)( 28,174)( 29,180)( 30,179)( 31,167)( 32,168)( 33,193)( 34,194)
( 35,310)( 36,309)( 37,300)( 38,299)( 39,319)( 40,320)( 41,298)( 42,297)
( 43,294)( 44,293)( 45,315)( 46,316)( 47,303)( 48,304)( 49,313)( 50,314)
( 51,318)( 52,317)( 53,292)( 54,291)( 55,312)( 56,311)( 57,305)( 58,306)
( 59,301)( 60,302)( 61,308)( 62,307)( 63,295)( 64,296)( 65,321)( 66,322)
( 67,278)( 68,277)( 69,268)( 70,267)( 71,287)( 72,288)( 73,266)( 74,265)
( 75,262)( 76,261)( 77,283)( 78,284)( 79,271)( 80,272)( 81,281)( 82,282)
( 83,286)( 84,285)( 85,260)( 86,259)( 87,280)( 88,279)( 89,273)( 90,274)
( 91,269)( 92,270)( 93,276)( 94,275)( 95,263)( 96,264)( 97,289)( 98,290)
( 99,246)(100,245)(101,236)(102,235)(103,255)(104,256)(105,234)(106,233)
(107,230)(108,229)(109,251)(110,252)(111,239)(112,240)(113,249)(114,250)
(115,254)(116,253)(117,228)(118,227)(119,248)(120,247)(121,241)(122,242)
(123,237)(124,238)(125,244)(126,243)(127,231)(128,232)(129,257)(130,258)
(131,214)(132,213)(133,204)(134,203)(135,223)(136,224)(137,202)(138,201)
(139,198)(140,197)(141,219)(142,220)(143,207)(144,208)(145,217)(146,218)
(147,222)(148,221)(149,196)(150,195)(151,216)(152,215)(153,209)(154,210)
(155,205)(156,206)(157,212)(158,211)(159,199)(160,200)(161,225)(162,226);;
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*s2*s3, s3*s1*s2*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*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)!( 3,182)( 4,181)( 5,172)( 6,171)( 7,191)( 8,192)( 9,170)
( 10,169)( 11,166)( 12,165)( 13,187)( 14,188)( 15,175)( 16,176)( 17,185)
( 18,186)( 19,190)( 20,189)( 21,164)( 22,163)( 23,184)( 24,183)( 25,177)
( 26,178)( 27,173)( 28,174)( 29,180)( 30,179)( 31,167)( 32,168)( 33,193)
( 34,194)( 35,310)( 36,309)( 37,300)( 38,299)( 39,319)( 40,320)( 41,298)
( 42,297)( 43,294)( 44,293)( 45,315)( 46,316)( 47,303)( 48,304)( 49,313)
( 50,314)( 51,318)( 52,317)( 53,292)( 54,291)( 55,312)( 56,311)( 57,305)
( 58,306)( 59,301)( 60,302)( 61,308)( 62,307)( 63,295)( 64,296)( 65,321)
( 66,322)( 67,278)( 68,277)( 69,268)( 70,267)( 71,287)( 72,288)( 73,266)
( 74,265)( 75,262)( 76,261)( 77,283)( 78,284)( 79,271)( 80,272)( 81,281)
( 82,282)( 83,286)( 84,285)( 85,260)( 86,259)( 87,280)( 88,279)( 89,273)
( 90,274)( 91,269)( 92,270)( 93,276)( 94,275)( 95,263)( 96,264)( 97,289)
( 98,290)( 99,246)(100,245)(101,236)(102,235)(103,255)(104,256)(105,234)
(106,233)(107,230)(108,229)(109,251)(110,252)(111,239)(112,240)(113,249)
(114,250)(115,254)(116,253)(117,228)(118,227)(119,248)(120,247)(121,241)
(122,242)(123,237)(124,238)(125,244)(126,243)(127,231)(128,232)(129,257)
(130,258)(131,214)(132,213)(133,204)(134,203)(135,223)(136,224)(137,202)
(138,201)(139,198)(140,197)(141,219)(142,220)(143,207)(144,208)(145,217)
(146,218)(147,222)(148,221)(149,196)(150,195)(151,216)(152,215)(153,209)
(154,210)(155,205)(156,206)(157,212)(158,211)(159,199)(160,200)(161,225)
(162,226);
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope