Polytope of Type {3,2,8,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,8,5}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240046)
Rank : 5
Schlafli Type : {3,2,8,5}
Number of vertices, edges, etc : 3, 3, 32, 80, 20
Order of s0s1s2s3s4 : 15
Order of s0s1s2s3s4s3s2s1 : 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 : {3,2,4,5}*960
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := ( 4, 6)( 5, 7)( 8, 10)( 9, 11)( 12, 14)( 13, 15)( 16, 18)( 17, 19)
( 20, 22)( 21, 23)( 24, 26)( 25, 27)( 28, 30)( 29, 31)( 32, 34)( 33, 35)
( 36, 38)( 37, 39)( 40, 42)( 41, 43)( 44, 46)( 45, 47)( 48, 50)( 49, 51)
( 52, 54)( 53, 55)( 56, 58)( 57, 59)( 60, 62)( 61, 63)( 64, 66)( 65, 67)
( 68, 70)( 69, 71)( 72, 74)( 73, 75)( 76, 78)( 77, 79)( 80, 82)( 81, 83)
( 84, 86)( 85, 87)( 88, 90)( 89, 91)( 92, 94)( 93, 95)( 96, 98)( 97, 99)
(100,102)(101,103)(104,106)(105,107)(108,110)(109,111)(112,114)(113,115)
(116,118)(117,119)(120,122)(121,123)(124,126)(125,127)(128,130)(129,131)
(132,134)(133,135)(136,138)(137,139)(140,142)(141,143)(144,146)(145,147)
(148,150)(149,151)(152,154)(153,155)(156,158)(157,159)(160,162)(161,163)
(164,166)(165,167)(168,170)(169,171)(172,174)(173,175)(176,178)(177,179)
(180,182)(181,183)(184,186)(185,187)(188,190)(189,191)(192,194)(193,195)
(196,198)(197,199)(200,202)(201,203)(204,206)(205,207)(208,210)(209,211)
(212,214)(213,215)(216,218)(217,219)(220,222)(221,223)(224,226)(225,227)
(228,230)(229,231)(232,234)(233,235)(236,238)(237,239)(240,242)(241,243)
(244,246)(245,247)(248,250)(249,251)(252,254)(253,255)(256,258)(257,259)
(260,262)(261,263)(264,266)(265,267)(268,270)(269,271)(272,274)(273,275)
(276,278)(277,279)(280,282)(281,283)(284,286)(285,287)(288,290)(289,291)
(292,294)(293,295)(296,298)(297,299)(300,302)(301,303)(304,306)(305,307)
(308,310)(309,311)(312,314)(313,315)(316,318)(317,319)(320,322)(321,323);;
s3 := ( 4,164)( 5,165)( 6,184)( 7,185)( 8,190)( 9,191)( 10,178)( 11,179)
( 12,173)( 13,172)( 14,192)( 15,193)( 16,183)( 17,182)( 18,170)( 19,171)
( 20,188)( 21,189)( 22,177)( 23,176)( 24,166)( 25,167)( 26,187)( 27,186)
( 28,180)( 29,181)( 30,168)( 31,169)( 32,174)( 33,175)( 34,194)( 35,195)
( 36,292)( 37,293)( 38,312)( 39,313)( 40,318)( 41,319)( 42,306)( 43,307)
( 44,301)( 45,300)( 46,320)( 47,321)( 48,311)( 49,310)( 50,298)( 51,299)
( 52,316)( 53,317)( 54,305)( 55,304)( 56,294)( 57,295)( 58,315)( 59,314)
( 60,308)( 61,309)( 62,296)( 63,297)( 64,302)( 65,303)( 66,322)( 67,323)
( 68,260)( 69,261)( 70,280)( 71,281)( 72,286)( 73,287)( 74,274)( 75,275)
( 76,269)( 77,268)( 78,288)( 79,289)( 80,279)( 81,278)( 82,266)( 83,267)
( 84,284)( 85,285)( 86,273)( 87,272)( 88,262)( 89,263)( 90,283)( 91,282)
( 92,276)( 93,277)( 94,264)( 95,265)( 96,270)( 97,271)( 98,290)( 99,291)
(100,228)(101,229)(102,248)(103,249)(104,254)(105,255)(106,242)(107,243)
(108,237)(109,236)(110,256)(111,257)(112,247)(113,246)(114,234)(115,235)
(116,252)(117,253)(118,241)(119,240)(120,230)(121,231)(122,251)(123,250)
(124,244)(125,245)(126,232)(127,233)(128,238)(129,239)(130,258)(131,259)
(132,196)(133,197)(134,216)(135,217)(136,222)(137,223)(138,210)(139,211)
(140,205)(141,204)(142,224)(143,225)(144,215)(145,214)(146,202)(147,203)
(148,220)(149,221)(150,209)(151,208)(152,198)(153,199)(154,219)(155,218)
(156,212)(157,213)(158,200)(159,201)(160,206)(161,207)(162,226)(163,227);;
s4 := ( 4,241)( 5,240)( 6,243)( 7,242)( 8,238)( 9,239)( 10,236)( 11,237)
( 12,234)( 13,235)( 14,232)( 15,233)( 16,229)( 17,228)( 18,231)( 19,230)
( 20,247)( 21,246)( 22,245)( 23,244)( 24,249)( 25,248)( 26,251)( 27,250)
( 28,252)( 29,253)( 30,254)( 31,255)( 32,258)( 33,259)( 34,256)( 35,257)
( 36,209)( 37,208)( 38,211)( 39,210)( 40,206)( 41,207)( 42,204)( 43,205)
( 44,202)( 45,203)( 46,200)( 47,201)( 48,197)( 49,196)( 50,199)( 51,198)
( 52,215)( 53,214)( 54,213)( 55,212)( 56,217)( 57,216)( 58,219)( 59,218)
( 60,220)( 61,221)( 62,222)( 63,223)( 64,226)( 65,227)( 66,224)( 67,225)
( 68,177)( 69,176)( 70,179)( 71,178)( 72,174)( 73,175)( 74,172)( 75,173)
( 76,170)( 77,171)( 78,168)( 79,169)( 80,165)( 81,164)( 82,167)( 83,166)
( 84,183)( 85,182)( 86,181)( 87,180)( 88,185)( 89,184)( 90,187)( 91,186)
( 92,188)( 93,189)( 94,190)( 95,191)( 96,194)( 97,195)( 98,192)( 99,193)
(100,305)(101,304)(102,307)(103,306)(104,302)(105,303)(106,300)(107,301)
(108,298)(109,299)(110,296)(111,297)(112,293)(113,292)(114,295)(115,294)
(116,311)(117,310)(118,309)(119,308)(120,313)(121,312)(122,315)(123,314)
(124,316)(125,317)(126,318)(127,319)(128,322)(129,323)(130,320)(131,321)
(132,273)(133,272)(134,275)(135,274)(136,270)(137,271)(138,268)(139,269)
(140,266)(141,267)(142,264)(143,265)(144,261)(145,260)(146,263)(147,262)
(148,279)(149,278)(150,277)(151,276)(152,281)(153,280)(154,283)(155,282)
(156,284)(157,285)(158,286)(159,287)(160,290)(161,291)(162,288)(163,289);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(323)!(2,3);
s1 := Sym(323)!(1,2);
s2 := Sym(323)!( 4, 6)( 5, 7)( 8, 10)( 9, 11)( 12, 14)( 13, 15)( 16, 18)
( 17, 19)( 20, 22)( 21, 23)( 24, 26)( 25, 27)( 28, 30)( 29, 31)( 32, 34)
( 33, 35)( 36, 38)( 37, 39)( 40, 42)( 41, 43)( 44, 46)( 45, 47)( 48, 50)
( 49, 51)( 52, 54)( 53, 55)( 56, 58)( 57, 59)( 60, 62)( 61, 63)( 64, 66)
( 65, 67)( 68, 70)( 69, 71)( 72, 74)( 73, 75)( 76, 78)( 77, 79)( 80, 82)
( 81, 83)( 84, 86)( 85, 87)( 88, 90)( 89, 91)( 92, 94)( 93, 95)( 96, 98)
( 97, 99)(100,102)(101,103)(104,106)(105,107)(108,110)(109,111)(112,114)
(113,115)(116,118)(117,119)(120,122)(121,123)(124,126)(125,127)(128,130)
(129,131)(132,134)(133,135)(136,138)(137,139)(140,142)(141,143)(144,146)
(145,147)(148,150)(149,151)(152,154)(153,155)(156,158)(157,159)(160,162)
(161,163)(164,166)(165,167)(168,170)(169,171)(172,174)(173,175)(176,178)
(177,179)(180,182)(181,183)(184,186)(185,187)(188,190)(189,191)(192,194)
(193,195)(196,198)(197,199)(200,202)(201,203)(204,206)(205,207)(208,210)
(209,211)(212,214)(213,215)(216,218)(217,219)(220,222)(221,223)(224,226)
(225,227)(228,230)(229,231)(232,234)(233,235)(236,238)(237,239)(240,242)
(241,243)(244,246)(245,247)(248,250)(249,251)(252,254)(253,255)(256,258)
(257,259)(260,262)(261,263)(264,266)(265,267)(268,270)(269,271)(272,274)
(273,275)(276,278)(277,279)(280,282)(281,283)(284,286)(285,287)(288,290)
(289,291)(292,294)(293,295)(296,298)(297,299)(300,302)(301,303)(304,306)
(305,307)(308,310)(309,311)(312,314)(313,315)(316,318)(317,319)(320,322)
(321,323);
s3 := Sym(323)!( 4,164)( 5,165)( 6,184)( 7,185)( 8,190)( 9,191)( 10,178)
( 11,179)( 12,173)( 13,172)( 14,192)( 15,193)( 16,183)( 17,182)( 18,170)
( 19,171)( 20,188)( 21,189)( 22,177)( 23,176)( 24,166)( 25,167)( 26,187)
( 27,186)( 28,180)( 29,181)( 30,168)( 31,169)( 32,174)( 33,175)( 34,194)
( 35,195)( 36,292)( 37,293)( 38,312)( 39,313)( 40,318)( 41,319)( 42,306)
( 43,307)( 44,301)( 45,300)( 46,320)( 47,321)( 48,311)( 49,310)( 50,298)
( 51,299)( 52,316)( 53,317)( 54,305)( 55,304)( 56,294)( 57,295)( 58,315)
( 59,314)( 60,308)( 61,309)( 62,296)( 63,297)( 64,302)( 65,303)( 66,322)
( 67,323)( 68,260)( 69,261)( 70,280)( 71,281)( 72,286)( 73,287)( 74,274)
( 75,275)( 76,269)( 77,268)( 78,288)( 79,289)( 80,279)( 81,278)( 82,266)
( 83,267)( 84,284)( 85,285)( 86,273)( 87,272)( 88,262)( 89,263)( 90,283)
( 91,282)( 92,276)( 93,277)( 94,264)( 95,265)( 96,270)( 97,271)( 98,290)
( 99,291)(100,228)(101,229)(102,248)(103,249)(104,254)(105,255)(106,242)
(107,243)(108,237)(109,236)(110,256)(111,257)(112,247)(113,246)(114,234)
(115,235)(116,252)(117,253)(118,241)(119,240)(120,230)(121,231)(122,251)
(123,250)(124,244)(125,245)(126,232)(127,233)(128,238)(129,239)(130,258)
(131,259)(132,196)(133,197)(134,216)(135,217)(136,222)(137,223)(138,210)
(139,211)(140,205)(141,204)(142,224)(143,225)(144,215)(145,214)(146,202)
(147,203)(148,220)(149,221)(150,209)(151,208)(152,198)(153,199)(154,219)
(155,218)(156,212)(157,213)(158,200)(159,201)(160,206)(161,207)(162,226)
(163,227);
s4 := Sym(323)!( 4,241)( 5,240)( 6,243)( 7,242)( 8,238)( 9,239)( 10,236)
( 11,237)( 12,234)( 13,235)( 14,232)( 15,233)( 16,229)( 17,228)( 18,231)
( 19,230)( 20,247)( 21,246)( 22,245)( 23,244)( 24,249)( 25,248)( 26,251)
( 27,250)( 28,252)( 29,253)( 30,254)( 31,255)( 32,258)( 33,259)( 34,256)
( 35,257)( 36,209)( 37,208)( 38,211)( 39,210)( 40,206)( 41,207)( 42,204)
( 43,205)( 44,202)( 45,203)( 46,200)( 47,201)( 48,197)( 49,196)( 50,199)
( 51,198)( 52,215)( 53,214)( 54,213)( 55,212)( 56,217)( 57,216)( 58,219)
( 59,218)( 60,220)( 61,221)( 62,222)( 63,223)( 64,226)( 65,227)( 66,224)
( 67,225)( 68,177)( 69,176)( 70,179)( 71,178)( 72,174)( 73,175)( 74,172)
( 75,173)( 76,170)( 77,171)( 78,168)( 79,169)( 80,165)( 81,164)( 82,167)
( 83,166)( 84,183)( 85,182)( 86,181)( 87,180)( 88,185)( 89,184)( 90,187)
( 91,186)( 92,188)( 93,189)( 94,190)( 95,191)( 96,194)( 97,195)( 98,192)
( 99,193)(100,305)(101,304)(102,307)(103,306)(104,302)(105,303)(106,300)
(107,301)(108,298)(109,299)(110,296)(111,297)(112,293)(113,292)(114,295)
(115,294)(116,311)(117,310)(118,309)(119,308)(120,313)(121,312)(122,315)
(123,314)(124,316)(125,317)(126,318)(127,319)(128,322)(129,323)(130,320)
(131,321)(132,273)(133,272)(134,275)(135,274)(136,270)(137,271)(138,268)
(139,269)(140,266)(141,267)(142,264)(143,265)(144,261)(145,260)(146,263)
(147,262)(148,279)(149,278)(150,277)(151,276)(152,281)(153,280)(154,283)
(155,282)(156,284)(157,285)(158,286)(159,287)(160,290)(161,291)(162,288)
(163,289);
poly := sub<Sym(323)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3 >;
to this polytope