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