Overview
- Group
- SmallGroup(1280,327682)
- Rank
- 4
- Schläfli Type
- {2,32,10}
- Vertices, edges, …
- 2, 32, 160, 10
- Order of s0s1s2s3
- 160
- 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
4-fold
5-fold
8-fold
10-fold
16-fold
20-fold
32-fold
40-fold
80-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 13, 18)( 14, 19)( 15, 20)( 16, 21)( 17, 22)( 23, 33)( 24, 34)( 25, 35)( 26, 36)( 27, 37)( 28, 38)( 29, 39)( 30, 40)( 31, 41)( 32, 42)( 43, 63)( 44, 64)( 45, 65)( 46, 66)( 47, 67)( 48, 68)( 49, 69)( 50, 70)( 51, 71)( 52, 72)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)( 58, 73)( 59, 74)( 60, 75)( 61, 76)( 62, 77)( 93, 98)( 94, 99)( 95,100)( 96,101)( 97,102)(103,113)(104,114)(105,115)(106,116)(107,117)(108,118)(109,119)(110,120)(111,121)(112,122)(123,143)(124,144)(125,145)(126,146)(127,147)(128,148)(129,149)(130,150)(131,151)(132,152)(133,158)(134,159)(135,160)(136,161)(137,162)(138,153)(139,154)(140,155)(141,156)(142,157)(163,203)(164,204)(165,205)(166,206)(167,207)(168,208)(169,209)(170,210)(171,211)(172,212)(173,218)(174,219)(175,220)(176,221)(177,222)(178,213)(179,214)(180,215)(181,216)(182,217)(183,233)(184,234)(185,235)(186,236)(187,237)(188,238)(189,239)(190,240)(191,241)(192,242)(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)(199,229)(200,230)(201,231)(202,232)(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)(250,290)(251,291)(252,292)(253,298)(254,299)(255,300)(256,301)(257,302)(258,293)(259,294)(260,295)(261,296)(262,297)(263,313)(264,314)(265,315)(266,316)(267,317)(268,318)(269,319)(270,320)(271,321)(272,322)(273,303)(274,304)(275,305)(276,306)(277,307)(278,308)(279,309)(280,310)(281,311)(282,312);; s2 := ( 3,243)( 4,247)( 5,246)( 6,245)( 7,244)( 8,248)( 9,252)( 10,251)( 11,250)( 12,249)( 13,258)( 14,262)( 15,261)( 16,260)( 17,259)( 18,253)( 19,257)( 20,256)( 21,255)( 22,254)( 23,273)( 24,277)( 25,276)( 26,275)( 27,274)( 28,278)( 29,282)( 30,281)( 31,280)( 32,279)( 33,263)( 34,267)( 35,266)( 36,265)( 37,264)( 38,268)( 39,272)( 40,271)( 41,270)( 42,269)( 43,303)( 44,307)( 45,306)( 46,305)( 47,304)( 48,308)( 49,312)( 50,311)( 51,310)( 52,309)( 53,318)( 54,322)( 55,321)( 56,320)( 57,319)( 58,313)( 59,317)( 60,316)( 61,315)( 62,314)( 63,283)( 64,287)( 65,286)( 66,285)( 67,284)( 68,288)( 69,292)( 70,291)( 71,290)( 72,289)( 73,298)( 74,302)( 75,301)( 76,300)( 77,299)( 78,293)( 79,297)( 80,296)( 81,295)( 82,294)( 83,163)( 84,167)( 85,166)( 86,165)( 87,164)( 88,168)( 89,172)( 90,171)( 91,170)( 92,169)( 93,178)( 94,182)( 95,181)( 96,180)( 97,179)( 98,173)( 99,177)(100,176)(101,175)(102,174)(103,193)(104,197)(105,196)(106,195)(107,194)(108,198)(109,202)(110,201)(111,200)(112,199)(113,183)(114,187)(115,186)(116,185)(117,184)(118,188)(119,192)(120,191)(121,190)(122,189)(123,223)(124,227)(125,226)(126,225)(127,224)(128,228)(129,232)(130,231)(131,230)(132,229)(133,238)(134,242)(135,241)(136,240)(137,239)(138,233)(139,237)(140,236)(141,235)(142,234)(143,203)(144,207)(145,206)(146,205)(147,204)(148,208)(149,212)(150,211)(151,210)(152,209)(153,218)(154,222)(155,221)(156,220)(157,219)(158,213)(159,217)(160,216)(161,215)(162,214);; s3 := ( 3, 84)( 4, 83)( 5, 87)( 6, 86)( 7, 85)( 8, 89)( 9, 88)( 10, 92)( 11, 91)( 12, 90)( 13, 94)( 14, 93)( 15, 97)( 16, 96)( 17, 95)( 18, 99)( 19, 98)( 20,102)( 21,101)( 22,100)( 23,104)( 24,103)( 25,107)( 26,106)( 27,105)( 28,109)( 29,108)( 30,112)( 31,111)( 32,110)( 33,114)( 34,113)( 35,117)( 36,116)( 37,115)( 38,119)( 39,118)( 40,122)( 41,121)( 42,120)( 43,124)( 44,123)( 45,127)( 46,126)( 47,125)( 48,129)( 49,128)( 50,132)( 51,131)( 52,130)( 53,134)( 54,133)( 55,137)( 56,136)( 57,135)( 58,139)( 59,138)( 60,142)( 61,141)( 62,140)( 63,144)( 64,143)( 65,147)( 66,146)( 67,145)( 68,149)( 69,148)( 70,152)( 71,151)( 72,150)( 73,154)( 74,153)( 75,157)( 76,156)( 77,155)( 78,159)( 79,158)( 80,162)( 81,161)( 82,160)(163,244)(164,243)(165,247)(166,246)(167,245)(168,249)(169,248)(170,252)(171,251)(172,250)(173,254)(174,253)(175,257)(176,256)(177,255)(178,259)(179,258)(180,262)(181,261)(182,260)(183,264)(184,263)(185,267)(186,266)(187,265)(188,269)(189,268)(190,272)(191,271)(192,270)(193,274)(194,273)(195,277)(196,276)(197,275)(198,279)(199,278)(200,282)(201,281)(202,280)(203,284)(204,283)(205,287)(206,286)(207,285)(208,289)(209,288)(210,292)(211,291)(212,290)(213,294)(214,293)(215,297)(216,296)(217,295)(218,299)(219,298)(220,302)(221,301)(222,300)(223,304)(224,303)(225,307)(226,306)(227,305)(228,309)(229,308)(230,312)(231,311)(232,310)(233,314)(234,313)(235,317)(236,316)(237,315)(238,319)(239,318)(240,322)(241,321)(242,320);; 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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(322)!(1,2); s1 := Sym(322)!( 13, 18)( 14, 19)( 15, 20)( 16, 21)( 17, 22)( 23, 33)( 24, 34)( 25, 35)( 26, 36)( 27, 37)( 28, 38)( 29, 39)( 30, 40)( 31, 41)( 32, 42)( 43, 63)( 44, 64)( 45, 65)( 46, 66)( 47, 67)( 48, 68)( 49, 69)( 50, 70)( 51, 71)( 52, 72)( 53, 78)( 54, 79)( 55, 80)( 56, 81)( 57, 82)( 58, 73)( 59, 74)( 60, 75)( 61, 76)( 62, 77)( 93, 98)( 94, 99)( 95,100)( 96,101)( 97,102)(103,113)(104,114)(105,115)(106,116)(107,117)(108,118)(109,119)(110,120)(111,121)(112,122)(123,143)(124,144)(125,145)(126,146)(127,147)(128,148)(129,149)(130,150)(131,151)(132,152)(133,158)(134,159)(135,160)(136,161)(137,162)(138,153)(139,154)(140,155)(141,156)(142,157)(163,203)(164,204)(165,205)(166,206)(167,207)(168,208)(169,209)(170,210)(171,211)(172,212)(173,218)(174,219)(175,220)(176,221)(177,222)(178,213)(179,214)(180,215)(181,216)(182,217)(183,233)(184,234)(185,235)(186,236)(187,237)(188,238)(189,239)(190,240)(191,241)(192,242)(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)(199,229)(200,230)(201,231)(202,232)(243,283)(244,284)(245,285)(246,286)(247,287)(248,288)(249,289)(250,290)(251,291)(252,292)(253,298)(254,299)(255,300)(256,301)(257,302)(258,293)(259,294)(260,295)(261,296)(262,297)(263,313)(264,314)(265,315)(266,316)(267,317)(268,318)(269,319)(270,320)(271,321)(272,322)(273,303)(274,304)(275,305)(276,306)(277,307)(278,308)(279,309)(280,310)(281,311)(282,312); s2 := Sym(322)!( 3,243)( 4,247)( 5,246)( 6,245)( 7,244)( 8,248)( 9,252)( 10,251)( 11,250)( 12,249)( 13,258)( 14,262)( 15,261)( 16,260)( 17,259)( 18,253)( 19,257)( 20,256)( 21,255)( 22,254)( 23,273)( 24,277)( 25,276)( 26,275)( 27,274)( 28,278)( 29,282)( 30,281)( 31,280)( 32,279)( 33,263)( 34,267)( 35,266)( 36,265)( 37,264)( 38,268)( 39,272)( 40,271)( 41,270)( 42,269)( 43,303)( 44,307)( 45,306)( 46,305)( 47,304)( 48,308)( 49,312)( 50,311)( 51,310)( 52,309)( 53,318)( 54,322)( 55,321)( 56,320)( 57,319)( 58,313)( 59,317)( 60,316)( 61,315)( 62,314)( 63,283)( 64,287)( 65,286)( 66,285)( 67,284)( 68,288)( 69,292)( 70,291)( 71,290)( 72,289)( 73,298)( 74,302)( 75,301)( 76,300)( 77,299)( 78,293)( 79,297)( 80,296)( 81,295)( 82,294)( 83,163)( 84,167)( 85,166)( 86,165)( 87,164)( 88,168)( 89,172)( 90,171)( 91,170)( 92,169)( 93,178)( 94,182)( 95,181)( 96,180)( 97,179)( 98,173)( 99,177)(100,176)(101,175)(102,174)(103,193)(104,197)(105,196)(106,195)(107,194)(108,198)(109,202)(110,201)(111,200)(112,199)(113,183)(114,187)(115,186)(116,185)(117,184)(118,188)(119,192)(120,191)(121,190)(122,189)(123,223)(124,227)(125,226)(126,225)(127,224)(128,228)(129,232)(130,231)(131,230)(132,229)(133,238)(134,242)(135,241)(136,240)(137,239)(138,233)(139,237)(140,236)(141,235)(142,234)(143,203)(144,207)(145,206)(146,205)(147,204)(148,208)(149,212)(150,211)(151,210)(152,209)(153,218)(154,222)(155,221)(156,220)(157,219)(158,213)(159,217)(160,216)(161,215)(162,214); s3 := Sym(322)!( 3, 84)( 4, 83)( 5, 87)( 6, 86)( 7, 85)( 8, 89)( 9, 88)( 10, 92)( 11, 91)( 12, 90)( 13, 94)( 14, 93)( 15, 97)( 16, 96)( 17, 95)( 18, 99)( 19, 98)( 20,102)( 21,101)( 22,100)( 23,104)( 24,103)( 25,107)( 26,106)( 27,105)( 28,109)( 29,108)( 30,112)( 31,111)( 32,110)( 33,114)( 34,113)( 35,117)( 36,116)( 37,115)( 38,119)( 39,118)( 40,122)( 41,121)( 42,120)( 43,124)( 44,123)( 45,127)( 46,126)( 47,125)( 48,129)( 49,128)( 50,132)( 51,131)( 52,130)( 53,134)( 54,133)( 55,137)( 56,136)( 57,135)( 58,139)( 59,138)( 60,142)( 61,141)( 62,140)( 63,144)( 64,143)( 65,147)( 66,146)( 67,145)( 68,149)( 69,148)( 70,152)( 71,151)( 72,150)( 73,154)( 74,153)( 75,157)( 76,156)( 77,155)( 78,159)( 79,158)( 80,162)( 81,161)( 82,160)(163,244)(164,243)(165,247)(166,246)(167,245)(168,249)(169,248)(170,252)(171,251)(172,250)(173,254)(174,253)(175,257)(176,256)(177,255)(178,259)(179,258)(180,262)(181,261)(182,260)(183,264)(184,263)(185,267)(186,266)(187,265)(188,269)(189,268)(190,272)(191,271)(192,270)(193,274)(194,273)(195,277)(196,276)(197,275)(198,279)(199,278)(200,282)(201,281)(202,280)(203,284)(204,283)(205,287)(206,286)(207,285)(208,289)(209,288)(210,292)(211,291)(212,290)(213,294)(214,293)(215,297)(216,296)(217,295)(218,299)(219,298)(220,302)(221,301)(222,300)(223,304)(224,303)(225,307)(226,306)(227,305)(228,309)(229,308)(230,312)(231,311)(232,310)(233,314)(234,313)(235,317)(236,316)(237,315)(238,319)(239,318)(240,322)(241,321)(242,320); 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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;