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