Polytope of Type {2,8,10}

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

to this polytope