Polytope of Type {2,4,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,20}*1280e
if this polytope has a name.
Group : SmallGroup(1280,1116454)
Rank : 4
Schlafli Type : {2,4,20}
Number of vertices, edges, etc : 2, 16, 160, 80
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 : {2,4,10}*640b
   4-fold quotients : {2,4,5}*320
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  3,179)(  4,180)(  5,182)(  6,181)(  7,184)(  8,183)(  9,185)( 10,186)
( 11,188)( 12,187)( 13,189)( 14,190)( 15,191)( 16,192)( 17,194)( 18,193)
( 19,164)( 20,163)( 21,165)( 22,166)( 23,167)( 24,168)( 25,170)( 26,169)
( 27,171)( 28,172)( 29,174)( 30,173)( 31,176)( 32,175)( 33,177)( 34,178)
( 35,211)( 36,212)( 37,214)( 38,213)( 39,216)( 40,215)( 41,217)( 42,218)
( 43,220)( 44,219)( 45,221)( 46,222)( 47,223)( 48,224)( 49,226)( 50,225)
( 51,196)( 52,195)( 53,197)( 54,198)( 55,199)( 56,200)( 57,202)( 58,201)
( 59,203)( 60,204)( 61,206)( 62,205)( 63,208)( 64,207)( 65,209)( 66,210)
( 67,243)( 68,244)( 69,246)( 70,245)( 71,248)( 72,247)( 73,249)( 74,250)
( 75,252)( 76,251)( 77,253)( 78,254)( 79,255)( 80,256)( 81,258)( 82,257)
( 83,228)( 84,227)( 85,229)( 86,230)( 87,231)( 88,232)( 89,234)( 90,233)
( 91,235)( 92,236)( 93,238)( 94,237)( 95,240)( 96,239)( 97,241)( 98,242)
( 99,275)(100,276)(101,278)(102,277)(103,280)(104,279)(105,281)(106,282)
(107,284)(108,283)(109,285)(110,286)(111,287)(112,288)(113,290)(114,289)
(115,260)(116,259)(117,261)(118,262)(119,263)(120,264)(121,266)(122,265)
(123,267)(124,268)(125,270)(126,269)(127,272)(128,271)(129,273)(130,274)
(131,307)(132,308)(133,310)(134,309)(135,312)(136,311)(137,313)(138,314)
(139,316)(140,315)(141,317)(142,318)(143,319)(144,320)(145,322)(146,321)
(147,292)(148,291)(149,293)(150,294)(151,295)(152,296)(153,298)(154,297)
(155,299)(156,300)(157,302)(158,301)(159,304)(160,303)(161,305)(162,306);;
s2 := (  3, 35)(  4, 36)(  5, 57)(  6, 58)(  7, 59)(  8, 60)(  9, 49)( 10, 50)
( 11, 44)( 12, 43)( 13, 65)( 14, 66)( 15, 52)( 16, 51)( 17, 41)( 18, 42)
( 19, 48)( 20, 47)( 21, 61)( 22, 62)( 23, 56)( 24, 55)( 25, 37)( 26, 38)
( 27, 39)( 28, 40)( 29, 53)( 30, 54)( 31, 63)( 32, 64)( 33, 45)( 34, 46)
( 67,131)( 68,132)( 69,153)( 70,154)( 71,155)( 72,156)( 73,145)( 74,146)
( 75,140)( 76,139)( 77,161)( 78,162)( 79,148)( 80,147)( 81,137)( 82,138)
( 83,144)( 84,143)( 85,157)( 86,158)( 87,152)( 88,151)( 89,133)( 90,134)
( 91,135)( 92,136)( 93,149)( 94,150)( 95,159)( 96,160)( 97,141)( 98,142)
(101,121)(102,122)(103,123)(104,124)(105,113)(106,114)(107,108)(109,129)
(110,130)(111,116)(112,115)(117,125)(118,126)(119,120)(163,196)(164,195)
(165,218)(166,217)(167,220)(168,219)(169,210)(170,209)(171,203)(172,204)
(173,226)(174,225)(175,211)(176,212)(177,202)(178,201)(179,207)(180,208)
(181,222)(182,221)(183,215)(184,216)(185,198)(186,197)(187,200)(188,199)
(189,214)(190,213)(191,224)(192,223)(193,206)(194,205)(227,292)(228,291)
(229,314)(230,313)(231,316)(232,315)(233,306)(234,305)(235,299)(236,300)
(237,322)(238,321)(239,307)(240,308)(241,298)(242,297)(243,303)(244,304)
(245,318)(246,317)(247,311)(248,312)(249,294)(250,293)(251,296)(252,295)
(253,310)(254,309)(255,320)(256,319)(257,302)(258,301)(259,260)(261,282)
(262,281)(263,284)(264,283)(265,274)(266,273)(269,290)(270,289)(271,275)
(272,276)(277,286)(278,285)(287,288);;
s3 := (  3,307)(  4,308)(  5,294)(  6,293)(  7,295)(  8,296)(  9,314)( 10,313)
( 11,306)( 12,305)( 13,319)( 14,320)( 15,317)( 16,318)( 17,300)( 18,299)
( 19,291)( 20,292)( 21,309)( 22,310)( 23,312)( 24,311)( 25,298)( 26,297)
( 27,321)( 28,322)( 29,303)( 30,304)( 31,301)( 32,302)( 33,315)( 34,316)
( 35,275)( 36,276)( 37,262)( 38,261)( 39,263)( 40,264)( 41,282)( 42,281)
( 43,274)( 44,273)( 45,287)( 46,288)( 47,285)( 48,286)( 49,268)( 50,267)
( 51,259)( 52,260)( 53,277)( 54,278)( 55,280)( 56,279)( 57,266)( 58,265)
( 59,289)( 60,290)( 61,271)( 62,272)( 63,269)( 64,270)( 65,283)( 66,284)
( 67,243)( 68,244)( 69,230)( 70,229)( 71,231)( 72,232)( 73,250)( 74,249)
( 75,242)( 76,241)( 77,255)( 78,256)( 79,253)( 80,254)( 81,236)( 82,235)
( 83,227)( 84,228)( 85,245)( 86,246)( 87,248)( 88,247)( 89,234)( 90,233)
( 91,257)( 92,258)( 93,239)( 94,240)( 95,237)( 96,238)( 97,251)( 98,252)
( 99,211)(100,212)(101,198)(102,197)(103,199)(104,200)(105,218)(106,217)
(107,210)(108,209)(109,223)(110,224)(111,221)(112,222)(113,204)(114,203)
(115,195)(116,196)(117,213)(118,214)(119,216)(120,215)(121,202)(122,201)
(123,225)(124,226)(125,207)(126,208)(127,205)(128,206)(129,219)(130,220)
(131,179)(132,180)(133,166)(134,165)(135,167)(136,168)(137,186)(138,185)
(139,178)(140,177)(141,191)(142,192)(143,189)(144,190)(145,172)(146,171)
(147,163)(148,164)(149,181)(150,182)(151,184)(152,183)(153,170)(154,169)
(155,193)(156,194)(157,175)(158,176)(159,173)(160,174)(161,187)(162,188);;
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*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3, 
s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(322)!(1,2);
s1 := Sym(322)!(  3,179)(  4,180)(  5,182)(  6,181)(  7,184)(  8,183)(  9,185)
( 10,186)( 11,188)( 12,187)( 13,189)( 14,190)( 15,191)( 16,192)( 17,194)
( 18,193)( 19,164)( 20,163)( 21,165)( 22,166)( 23,167)( 24,168)( 25,170)
( 26,169)( 27,171)( 28,172)( 29,174)( 30,173)( 31,176)( 32,175)( 33,177)
( 34,178)( 35,211)( 36,212)( 37,214)( 38,213)( 39,216)( 40,215)( 41,217)
( 42,218)( 43,220)( 44,219)( 45,221)( 46,222)( 47,223)( 48,224)( 49,226)
( 50,225)( 51,196)( 52,195)( 53,197)( 54,198)( 55,199)( 56,200)( 57,202)
( 58,201)( 59,203)( 60,204)( 61,206)( 62,205)( 63,208)( 64,207)( 65,209)
( 66,210)( 67,243)( 68,244)( 69,246)( 70,245)( 71,248)( 72,247)( 73,249)
( 74,250)( 75,252)( 76,251)( 77,253)( 78,254)( 79,255)( 80,256)( 81,258)
( 82,257)( 83,228)( 84,227)( 85,229)( 86,230)( 87,231)( 88,232)( 89,234)
( 90,233)( 91,235)( 92,236)( 93,238)( 94,237)( 95,240)( 96,239)( 97,241)
( 98,242)( 99,275)(100,276)(101,278)(102,277)(103,280)(104,279)(105,281)
(106,282)(107,284)(108,283)(109,285)(110,286)(111,287)(112,288)(113,290)
(114,289)(115,260)(116,259)(117,261)(118,262)(119,263)(120,264)(121,266)
(122,265)(123,267)(124,268)(125,270)(126,269)(127,272)(128,271)(129,273)
(130,274)(131,307)(132,308)(133,310)(134,309)(135,312)(136,311)(137,313)
(138,314)(139,316)(140,315)(141,317)(142,318)(143,319)(144,320)(145,322)
(146,321)(147,292)(148,291)(149,293)(150,294)(151,295)(152,296)(153,298)
(154,297)(155,299)(156,300)(157,302)(158,301)(159,304)(160,303)(161,305)
(162,306);
s2 := Sym(322)!(  3, 35)(  4, 36)(  5, 57)(  6, 58)(  7, 59)(  8, 60)(  9, 49)
( 10, 50)( 11, 44)( 12, 43)( 13, 65)( 14, 66)( 15, 52)( 16, 51)( 17, 41)
( 18, 42)( 19, 48)( 20, 47)( 21, 61)( 22, 62)( 23, 56)( 24, 55)( 25, 37)
( 26, 38)( 27, 39)( 28, 40)( 29, 53)( 30, 54)( 31, 63)( 32, 64)( 33, 45)
( 34, 46)( 67,131)( 68,132)( 69,153)( 70,154)( 71,155)( 72,156)( 73,145)
( 74,146)( 75,140)( 76,139)( 77,161)( 78,162)( 79,148)( 80,147)( 81,137)
( 82,138)( 83,144)( 84,143)( 85,157)( 86,158)( 87,152)( 88,151)( 89,133)
( 90,134)( 91,135)( 92,136)( 93,149)( 94,150)( 95,159)( 96,160)( 97,141)
( 98,142)(101,121)(102,122)(103,123)(104,124)(105,113)(106,114)(107,108)
(109,129)(110,130)(111,116)(112,115)(117,125)(118,126)(119,120)(163,196)
(164,195)(165,218)(166,217)(167,220)(168,219)(169,210)(170,209)(171,203)
(172,204)(173,226)(174,225)(175,211)(176,212)(177,202)(178,201)(179,207)
(180,208)(181,222)(182,221)(183,215)(184,216)(185,198)(186,197)(187,200)
(188,199)(189,214)(190,213)(191,224)(192,223)(193,206)(194,205)(227,292)
(228,291)(229,314)(230,313)(231,316)(232,315)(233,306)(234,305)(235,299)
(236,300)(237,322)(238,321)(239,307)(240,308)(241,298)(242,297)(243,303)
(244,304)(245,318)(246,317)(247,311)(248,312)(249,294)(250,293)(251,296)
(252,295)(253,310)(254,309)(255,320)(256,319)(257,302)(258,301)(259,260)
(261,282)(262,281)(263,284)(264,283)(265,274)(266,273)(269,290)(270,289)
(271,275)(272,276)(277,286)(278,285)(287,288);
s3 := Sym(322)!(  3,307)(  4,308)(  5,294)(  6,293)(  7,295)(  8,296)(  9,314)
( 10,313)( 11,306)( 12,305)( 13,319)( 14,320)( 15,317)( 16,318)( 17,300)
( 18,299)( 19,291)( 20,292)( 21,309)( 22,310)( 23,312)( 24,311)( 25,298)
( 26,297)( 27,321)( 28,322)( 29,303)( 30,304)( 31,301)( 32,302)( 33,315)
( 34,316)( 35,275)( 36,276)( 37,262)( 38,261)( 39,263)( 40,264)( 41,282)
( 42,281)( 43,274)( 44,273)( 45,287)( 46,288)( 47,285)( 48,286)( 49,268)
( 50,267)( 51,259)( 52,260)( 53,277)( 54,278)( 55,280)( 56,279)( 57,266)
( 58,265)( 59,289)( 60,290)( 61,271)( 62,272)( 63,269)( 64,270)( 65,283)
( 66,284)( 67,243)( 68,244)( 69,230)( 70,229)( 71,231)( 72,232)( 73,250)
( 74,249)( 75,242)( 76,241)( 77,255)( 78,256)( 79,253)( 80,254)( 81,236)
( 82,235)( 83,227)( 84,228)( 85,245)( 86,246)( 87,248)( 88,247)( 89,234)
( 90,233)( 91,257)( 92,258)( 93,239)( 94,240)( 95,237)( 96,238)( 97,251)
( 98,252)( 99,211)(100,212)(101,198)(102,197)(103,199)(104,200)(105,218)
(106,217)(107,210)(108,209)(109,223)(110,224)(111,221)(112,222)(113,204)
(114,203)(115,195)(116,196)(117,213)(118,214)(119,216)(120,215)(121,202)
(122,201)(123,225)(124,226)(125,207)(126,208)(127,205)(128,206)(129,219)
(130,220)(131,179)(132,180)(133,166)(134,165)(135,167)(136,168)(137,186)
(138,185)(139,178)(140,177)(141,191)(142,192)(143,189)(144,190)(145,172)
(146,171)(147,163)(148,164)(149,181)(150,182)(151,184)(152,183)(153,170)
(154,169)(155,193)(156,194)(157,175)(158,176)(159,173)(160,174)(161,187)
(162,188);
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*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3, 
s1*s2*s3*s2*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s3*s2*s3*s2 >;

to this polytope