Overview
- Group
- SmallGroup(640,21461)
- Rank
- 4
- Schläfli Type
- {2,5,10}
- Vertices, edges, …
- 2, 16, 80, 32
- Order of s0s1s2s3
- 8
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
Covers minimal covers in bold
2-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,163)( 4,164)( 5,183)( 6,184)( 7,189)( 8,190)( 9,177)( 10,178)( 11,172)( 12,171)( 13,191)( 14,192)( 15,182)( 16,181)( 17,169)( 18,170)( 19,187)( 20,188)( 21,176)( 22,175)( 23,165)( 24,166)( 25,186)( 26,185)( 27,179)( 28,180)( 29,167)( 30,168)( 31,173)( 32,174)( 33,193)( 34,194)( 35,291)( 36,292)( 37,311)( 38,312)( 39,317)( 40,318)( 41,305)( 42,306)( 43,300)( 44,299)( 45,319)( 46,320)( 47,310)( 48,309)( 49,297)( 50,298)( 51,315)( 52,316)( 53,304)( 54,303)( 55,293)( 56,294)( 57,314)( 58,313)( 59,307)( 60,308)( 61,295)( 62,296)( 63,301)( 64,302)( 65,321)( 66,322)( 67,259)( 68,260)( 69,279)( 70,280)( 71,285)( 72,286)( 73,273)( 74,274)( 75,268)( 76,267)( 77,287)( 78,288)( 79,278)( 80,277)( 81,265)( 82,266)( 83,283)( 84,284)( 85,272)( 86,271)( 87,261)( 88,262)( 89,282)( 90,281)( 91,275)( 92,276)( 93,263)( 94,264)( 95,269)( 96,270)( 97,289)( 98,290)( 99,227)(100,228)(101,247)(102,248)(103,253)(104,254)(105,241)(106,242)(107,236)(108,235)(109,255)(110,256)(111,246)(112,245)(113,233)(114,234)(115,251)(116,252)(117,240)(118,239)(119,229)(120,230)(121,250)(122,249)(123,243)(124,244)(125,231)(126,232)(127,237)(128,238)(129,257)(130,258)(131,195)(132,196)(133,215)(134,216)(135,221)(136,222)(137,209)(138,210)(139,204)(140,203)(141,223)(142,224)(143,214)(144,213)(145,201)(146,202)(147,219)(148,220)(149,208)(150,207)(151,197)(152,198)(153,218)(154,217)(155,211)(156,212)(157,199)(158,200)(159,205)(160,206)(161,225)(162,226);; s2 := ( 3,195)( 4,196)( 5,225)( 6,226)( 7,200)( 8,199)( 9,221)( 10,222)( 11,208)( 12,207)( 13,213)( 14,214)( 15,204)( 16,203)( 17,218)( 18,217)( 19,216)( 20,215)( 21,205)( 22,206)( 23,212)( 24,211)( 25,210)( 26,209)( 27,219)( 28,220)( 29,201)( 30,202)( 31,224)( 32,223)( 33,197)( 34,198)( 35,163)( 36,164)( 37,193)( 38,194)( 39,168)( 40,167)( 41,189)( 42,190)( 43,176)( 44,175)( 45,181)( 46,182)( 47,172)( 48,171)( 49,186)( 50,185)( 51,184)( 52,183)( 53,173)( 54,174)( 55,180)( 56,179)( 57,178)( 58,177)( 59,187)( 60,188)( 61,169)( 62,170)( 63,192)( 64,191)( 65,165)( 66,166)( 67,291)( 68,292)( 69,321)( 70,322)( 71,296)( 72,295)( 73,317)( 74,318)( 75,304)( 76,303)( 77,309)( 78,310)( 79,300)( 80,299)( 81,314)( 82,313)( 83,312)( 84,311)( 85,301)( 86,302)( 87,308)( 88,307)( 89,306)( 90,305)( 91,315)( 92,316)( 93,297)( 94,298)( 95,320)( 96,319)( 97,293)( 98,294)( 99,259)(100,260)(101,289)(102,290)(103,264)(104,263)(105,285)(106,286)(107,272)(108,271)(109,277)(110,278)(111,268)(112,267)(113,282)(114,281)(115,280)(116,279)(117,269)(118,270)(119,276)(120,275)(121,274)(122,273)(123,283)(124,284)(125,265)(126,266)(127,288)(128,287)(129,261)(130,262)(131,227)(132,228)(133,257)(134,258)(135,232)(136,231)(137,253)(138,254)(139,240)(140,239)(141,245)(142,246)(143,236)(144,235)(145,250)(146,249)(147,248)(148,247)(149,237)(150,238)(151,244)(152,243)(153,242)(154,241)(155,251)(156,252)(157,233)(158,234)(159,256)(160,255)(161,229)(162,230);; s3 := ( 3,194)( 4,193)( 5,173)( 6,174)( 7,167)( 8,168)( 9,180)( 10,179)( 11,185)( 12,186)( 13,165)( 14,166)( 15,176)( 16,175)( 17,188)( 18,187)( 19,170)( 20,169)( 21,182)( 22,181)( 23,191)( 24,192)( 25,171)( 26,172)( 27,178)( 28,177)( 29,189)( 30,190)( 31,183)( 32,184)( 33,164)( 34,163)( 35,322)( 36,321)( 37,301)( 38,302)( 39,295)( 40,296)( 41,308)( 42,307)( 43,313)( 44,314)( 45,293)( 46,294)( 47,304)( 48,303)( 49,316)( 50,315)( 51,298)( 52,297)( 53,310)( 54,309)( 55,319)( 56,320)( 57,299)( 58,300)( 59,306)( 60,305)( 61,317)( 62,318)( 63,311)( 64,312)( 65,292)( 66,291)( 67,290)( 68,289)( 69,269)( 70,270)( 71,263)( 72,264)( 73,276)( 74,275)( 75,281)( 76,282)( 77,261)( 78,262)( 79,272)( 80,271)( 81,284)( 82,283)( 83,266)( 84,265)( 85,278)( 86,277)( 87,287)( 88,288)( 89,267)( 90,268)( 91,274)( 92,273)( 93,285)( 94,286)( 95,279)( 96,280)( 97,260)( 98,259)( 99,258)(100,257)(101,237)(102,238)(103,231)(104,232)(105,244)(106,243)(107,249)(108,250)(109,229)(110,230)(111,240)(112,239)(113,252)(114,251)(115,234)(116,233)(117,246)(118,245)(119,255)(120,256)(121,235)(122,236)(123,242)(124,241)(125,253)(126,254)(127,247)(128,248)(129,228)(130,227)(131,226)(132,225)(133,205)(134,206)(135,199)(136,200)(137,212)(138,211)(139,217)(140,218)(141,197)(142,198)(143,208)(144,207)(145,220)(146,219)(147,202)(148,201)(149,214)(150,213)(151,223)(152,224)(153,203)(154,204)(155,210)(156,209)(157,221)(158,222)(159,215)(160,216)(161,196)(162,195);; 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, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(322)!(1,2); s1 := Sym(322)!( 3,163)( 4,164)( 5,183)( 6,184)( 7,189)( 8,190)( 9,177)( 10,178)( 11,172)( 12,171)( 13,191)( 14,192)( 15,182)( 16,181)( 17,169)( 18,170)( 19,187)( 20,188)( 21,176)( 22,175)( 23,165)( 24,166)( 25,186)( 26,185)( 27,179)( 28,180)( 29,167)( 30,168)( 31,173)( 32,174)( 33,193)( 34,194)( 35,291)( 36,292)( 37,311)( 38,312)( 39,317)( 40,318)( 41,305)( 42,306)( 43,300)( 44,299)( 45,319)( 46,320)( 47,310)( 48,309)( 49,297)( 50,298)( 51,315)( 52,316)( 53,304)( 54,303)( 55,293)( 56,294)( 57,314)( 58,313)( 59,307)( 60,308)( 61,295)( 62,296)( 63,301)( 64,302)( 65,321)( 66,322)( 67,259)( 68,260)( 69,279)( 70,280)( 71,285)( 72,286)( 73,273)( 74,274)( 75,268)( 76,267)( 77,287)( 78,288)( 79,278)( 80,277)( 81,265)( 82,266)( 83,283)( 84,284)( 85,272)( 86,271)( 87,261)( 88,262)( 89,282)( 90,281)( 91,275)( 92,276)( 93,263)( 94,264)( 95,269)( 96,270)( 97,289)( 98,290)( 99,227)(100,228)(101,247)(102,248)(103,253)(104,254)(105,241)(106,242)(107,236)(108,235)(109,255)(110,256)(111,246)(112,245)(113,233)(114,234)(115,251)(116,252)(117,240)(118,239)(119,229)(120,230)(121,250)(122,249)(123,243)(124,244)(125,231)(126,232)(127,237)(128,238)(129,257)(130,258)(131,195)(132,196)(133,215)(134,216)(135,221)(136,222)(137,209)(138,210)(139,204)(140,203)(141,223)(142,224)(143,214)(144,213)(145,201)(146,202)(147,219)(148,220)(149,208)(150,207)(151,197)(152,198)(153,218)(154,217)(155,211)(156,212)(157,199)(158,200)(159,205)(160,206)(161,225)(162,226); s2 := Sym(322)!( 3,195)( 4,196)( 5,225)( 6,226)( 7,200)( 8,199)( 9,221)( 10,222)( 11,208)( 12,207)( 13,213)( 14,214)( 15,204)( 16,203)( 17,218)( 18,217)( 19,216)( 20,215)( 21,205)( 22,206)( 23,212)( 24,211)( 25,210)( 26,209)( 27,219)( 28,220)( 29,201)( 30,202)( 31,224)( 32,223)( 33,197)( 34,198)( 35,163)( 36,164)( 37,193)( 38,194)( 39,168)( 40,167)( 41,189)( 42,190)( 43,176)( 44,175)( 45,181)( 46,182)( 47,172)( 48,171)( 49,186)( 50,185)( 51,184)( 52,183)( 53,173)( 54,174)( 55,180)( 56,179)( 57,178)( 58,177)( 59,187)( 60,188)( 61,169)( 62,170)( 63,192)( 64,191)( 65,165)( 66,166)( 67,291)( 68,292)( 69,321)( 70,322)( 71,296)( 72,295)( 73,317)( 74,318)( 75,304)( 76,303)( 77,309)( 78,310)( 79,300)( 80,299)( 81,314)( 82,313)( 83,312)( 84,311)( 85,301)( 86,302)( 87,308)( 88,307)( 89,306)( 90,305)( 91,315)( 92,316)( 93,297)( 94,298)( 95,320)( 96,319)( 97,293)( 98,294)( 99,259)(100,260)(101,289)(102,290)(103,264)(104,263)(105,285)(106,286)(107,272)(108,271)(109,277)(110,278)(111,268)(112,267)(113,282)(114,281)(115,280)(116,279)(117,269)(118,270)(119,276)(120,275)(121,274)(122,273)(123,283)(124,284)(125,265)(126,266)(127,288)(128,287)(129,261)(130,262)(131,227)(132,228)(133,257)(134,258)(135,232)(136,231)(137,253)(138,254)(139,240)(140,239)(141,245)(142,246)(143,236)(144,235)(145,250)(146,249)(147,248)(148,247)(149,237)(150,238)(151,244)(152,243)(153,242)(154,241)(155,251)(156,252)(157,233)(158,234)(159,256)(160,255)(161,229)(162,230); s3 := Sym(322)!( 3,194)( 4,193)( 5,173)( 6,174)( 7,167)( 8,168)( 9,180)( 10,179)( 11,185)( 12,186)( 13,165)( 14,166)( 15,176)( 16,175)( 17,188)( 18,187)( 19,170)( 20,169)( 21,182)( 22,181)( 23,191)( 24,192)( 25,171)( 26,172)( 27,178)( 28,177)( 29,189)( 30,190)( 31,183)( 32,184)( 33,164)( 34,163)( 35,322)( 36,321)( 37,301)( 38,302)( 39,295)( 40,296)( 41,308)( 42,307)( 43,313)( 44,314)( 45,293)( 46,294)( 47,304)( 48,303)( 49,316)( 50,315)( 51,298)( 52,297)( 53,310)( 54,309)( 55,319)( 56,320)( 57,299)( 58,300)( 59,306)( 60,305)( 61,317)( 62,318)( 63,311)( 64,312)( 65,292)( 66,291)( 67,290)( 68,289)( 69,269)( 70,270)( 71,263)( 72,264)( 73,276)( 74,275)( 75,281)( 76,282)( 77,261)( 78,262)( 79,272)( 80,271)( 81,284)( 82,283)( 83,266)( 84,265)( 85,278)( 86,277)( 87,287)( 88,288)( 89,267)( 90,268)( 91,274)( 92,273)( 93,285)( 94,286)( 95,279)( 96,280)( 97,260)( 98,259)( 99,258)(100,257)(101,237)(102,238)(103,231)(104,232)(105,244)(106,243)(107,249)(108,250)(109,229)(110,230)(111,240)(112,239)(113,252)(114,251)(115,234)(116,233)(117,246)(118,245)(119,255)(120,256)(121,235)(122,236)(123,242)(124,241)(125,253)(126,254)(127,247)(128,248)(129,228)(130,227)(131,226)(132,225)(133,205)(134,206)(135,199)(136,200)(137,212)(138,211)(139,217)(140,218)(141,197)(142,198)(143,208)(144,207)(145,220)(146,219)(147,202)(148,201)(149,214)(150,213)(151,223)(152,224)(153,203)(154,204)(155,210)(156,209)(157,221)(158,222)(159,215)(160,216)(161,196)(162,195); 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, s1*s2*s3*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2 >;