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