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