Overview
- Group
- SmallGroup(1920,240142)
- Rank
- 5
- Schläfli Type
- {2,3,6,20}
- Vertices, edges, …
- 2, 4, 12, 80, 20
- Order of s0s1s2s3s4
- 20
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
5-fold
10-fold
20-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 51)( 32, 53)( 33, 52)( 34, 54)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 59)( 40, 61)( 41, 60)( 42, 62)( 64, 65)( 68, 69)( 72, 73)( 76, 77)( 80, 81)( 83,103)( 84,105)( 85,104)( 86,106)( 87,107)( 88,109)( 89,108)( 90,110)( 91,111)( 92,113)( 93,112)( 94,114)( 95,115)( 96,117)( 97,116)( 98,118)( 99,119)(100,121)(101,120)(102,122)(124,125)(128,129)(132,133)(136,137)(140,141)(143,163)(144,165)(145,164)(146,166)(147,167)(148,169)(149,168)(150,170)(151,171)(152,173)(153,172)(154,174)(155,175)(156,177)(157,176)(158,178)(159,179)(160,181)(161,180)(162,182)(184,185)(188,189)(192,193)(196,197)(200,201)(203,223)(204,225)(205,224)(206,226)(207,227)(208,229)(209,228)(210,230)(211,231)(212,233)(213,232)(214,234)(215,235)(216,237)(217,236)(218,238)(219,239)(220,241)(221,240)(222,242);; s2 := ( 3, 23)( 4, 24)( 5, 26)( 6, 25)( 7, 27)( 8, 28)( 9, 30)( 10, 29)( 11, 31)( 12, 32)( 13, 34)( 14, 33)( 15, 35)( 16, 36)( 17, 38)( 18, 37)( 19, 39)( 20, 40)( 21, 42)( 22, 41)( 45, 46)( 49, 50)( 53, 54)( 57, 58)( 61, 62)( 63, 83)( 64, 84)( 65, 86)( 66, 85)( 67, 87)( 68, 88)( 69, 90)( 70, 89)( 71, 91)( 72, 92)( 73, 94)( 74, 93)( 75, 95)( 76, 96)( 77, 98)( 78, 97)( 79, 99)( 80,100)( 81,102)( 82,101)(105,106)(109,110)(113,114)(117,118)(121,122)(123,143)(124,144)(125,146)(126,145)(127,147)(128,148)(129,150)(130,149)(131,151)(132,152)(133,154)(134,153)(135,155)(136,156)(137,158)(138,157)(139,159)(140,160)(141,162)(142,161)(165,166)(169,170)(173,174)(177,178)(181,182)(183,203)(184,204)(185,206)(186,205)(187,207)(188,208)(189,210)(190,209)(191,211)(192,212)(193,214)(194,213)(195,215)(196,216)(197,218)(198,217)(199,219)(200,220)(201,222)(202,221)(225,226)(229,230)(233,234)(237,238)(241,242);; s3 := ( 3, 6)( 7, 22)( 8, 20)( 9, 21)( 10, 19)( 11, 18)( 12, 16)( 13, 17)( 14, 15)( 23, 46)( 24, 44)( 25, 45)( 26, 43)( 27, 62)( 28, 60)( 29, 61)( 30, 59)( 31, 58)( 32, 56)( 33, 57)( 34, 55)( 35, 54)( 36, 52)( 37, 53)( 38, 51)( 39, 50)( 40, 48)( 41, 49)( 42, 47)( 63, 66)( 67, 82)( 68, 80)( 69, 81)( 70, 79)( 71, 78)( 72, 76)( 73, 77)( 74, 75)( 83,106)( 84,104)( 85,105)( 86,103)( 87,122)( 88,120)( 89,121)( 90,119)( 91,118)( 92,116)( 93,117)( 94,115)( 95,114)( 96,112)( 97,113)( 98,111)( 99,110)(100,108)(101,109)(102,107)(123,186)(124,184)(125,185)(126,183)(127,202)(128,200)(129,201)(130,199)(131,198)(132,196)(133,197)(134,195)(135,194)(136,192)(137,193)(138,191)(139,190)(140,188)(141,189)(142,187)(143,226)(144,224)(145,225)(146,223)(147,242)(148,240)(149,241)(150,239)(151,238)(152,236)(153,237)(154,235)(155,234)(156,232)(157,233)(158,231)(159,230)(160,228)(161,229)(162,227)(163,206)(164,204)(165,205)(166,203)(167,222)(168,220)(169,221)(170,219)(171,218)(172,216)(173,217)(174,215)(175,214)(176,212)(177,213)(178,211)(179,210)(180,208)(181,209)(182,207);; s4 := ( 3,127)( 4,128)( 5,129)( 6,130)( 7,123)( 8,124)( 9,125)( 10,126)( 11,139)( 12,140)( 13,141)( 14,142)( 15,135)( 16,136)( 17,137)( 18,138)( 19,131)( 20,132)( 21,133)( 22,134)( 23,147)( 24,148)( 25,149)( 26,150)( 27,143)( 28,144)( 29,145)( 30,146)( 31,159)( 32,160)( 33,161)( 34,162)( 35,155)( 36,156)( 37,157)( 38,158)( 39,151)( 40,152)( 41,153)( 42,154)( 43,167)( 44,168)( 45,169)( 46,170)( 47,163)( 48,164)( 49,165)( 50,166)( 51,179)( 52,180)( 53,181)( 54,182)( 55,175)( 56,176)( 57,177)( 58,178)( 59,171)( 60,172)( 61,173)( 62,174)( 63,187)( 64,188)( 65,189)( 66,190)( 67,183)( 68,184)( 69,185)( 70,186)( 71,199)( 72,200)( 73,201)( 74,202)( 75,195)( 76,196)( 77,197)( 78,198)( 79,191)( 80,192)( 81,193)( 82,194)( 83,207)( 84,208)( 85,209)( 86,210)( 87,203)( 88,204)( 89,205)( 90,206)( 91,219)( 92,220)( 93,221)( 94,222)( 95,215)( 96,216)( 97,217)( 98,218)( 99,211)(100,212)(101,213)(102,214)(103,227)(104,228)(105,229)(106,230)(107,223)(108,224)(109,225)(110,226)(111,239)(112,240)(113,241)(114,242)(115,235)(116,236)(117,237)(118,238)(119,231)(120,232)(121,233)(122,234);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(242)!(1,2); s1 := Sym(242)!( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 47)( 28, 49)( 29, 48)( 30, 50)( 31, 51)( 32, 53)( 33, 52)( 34, 54)( 35, 55)( 36, 57)( 37, 56)( 38, 58)( 39, 59)( 40, 61)( 41, 60)( 42, 62)( 64, 65)( 68, 69)( 72, 73)( 76, 77)( 80, 81)( 83,103)( 84,105)( 85,104)( 86,106)( 87,107)( 88,109)( 89,108)( 90,110)( 91,111)( 92,113)( 93,112)( 94,114)( 95,115)( 96,117)( 97,116)( 98,118)( 99,119)(100,121)(101,120)(102,122)(124,125)(128,129)(132,133)(136,137)(140,141)(143,163)(144,165)(145,164)(146,166)(147,167)(148,169)(149,168)(150,170)(151,171)(152,173)(153,172)(154,174)(155,175)(156,177)(157,176)(158,178)(159,179)(160,181)(161,180)(162,182)(184,185)(188,189)(192,193)(196,197)(200,201)(203,223)(204,225)(205,224)(206,226)(207,227)(208,229)(209,228)(210,230)(211,231)(212,233)(213,232)(214,234)(215,235)(216,237)(217,236)(218,238)(219,239)(220,241)(221,240)(222,242); s2 := Sym(242)!( 3, 23)( 4, 24)( 5, 26)( 6, 25)( 7, 27)( 8, 28)( 9, 30)( 10, 29)( 11, 31)( 12, 32)( 13, 34)( 14, 33)( 15, 35)( 16, 36)( 17, 38)( 18, 37)( 19, 39)( 20, 40)( 21, 42)( 22, 41)( 45, 46)( 49, 50)( 53, 54)( 57, 58)( 61, 62)( 63, 83)( 64, 84)( 65, 86)( 66, 85)( 67, 87)( 68, 88)( 69, 90)( 70, 89)( 71, 91)( 72, 92)( 73, 94)( 74, 93)( 75, 95)( 76, 96)( 77, 98)( 78, 97)( 79, 99)( 80,100)( 81,102)( 82,101)(105,106)(109,110)(113,114)(117,118)(121,122)(123,143)(124,144)(125,146)(126,145)(127,147)(128,148)(129,150)(130,149)(131,151)(132,152)(133,154)(134,153)(135,155)(136,156)(137,158)(138,157)(139,159)(140,160)(141,162)(142,161)(165,166)(169,170)(173,174)(177,178)(181,182)(183,203)(184,204)(185,206)(186,205)(187,207)(188,208)(189,210)(190,209)(191,211)(192,212)(193,214)(194,213)(195,215)(196,216)(197,218)(198,217)(199,219)(200,220)(201,222)(202,221)(225,226)(229,230)(233,234)(237,238)(241,242); s3 := Sym(242)!( 3, 6)( 7, 22)( 8, 20)( 9, 21)( 10, 19)( 11, 18)( 12, 16)( 13, 17)( 14, 15)( 23, 46)( 24, 44)( 25, 45)( 26, 43)( 27, 62)( 28, 60)( 29, 61)( 30, 59)( 31, 58)( 32, 56)( 33, 57)( 34, 55)( 35, 54)( 36, 52)( 37, 53)( 38, 51)( 39, 50)( 40, 48)( 41, 49)( 42, 47)( 63, 66)( 67, 82)( 68, 80)( 69, 81)( 70, 79)( 71, 78)( 72, 76)( 73, 77)( 74, 75)( 83,106)( 84,104)( 85,105)( 86,103)( 87,122)( 88,120)( 89,121)( 90,119)( 91,118)( 92,116)( 93,117)( 94,115)( 95,114)( 96,112)( 97,113)( 98,111)( 99,110)(100,108)(101,109)(102,107)(123,186)(124,184)(125,185)(126,183)(127,202)(128,200)(129,201)(130,199)(131,198)(132,196)(133,197)(134,195)(135,194)(136,192)(137,193)(138,191)(139,190)(140,188)(141,189)(142,187)(143,226)(144,224)(145,225)(146,223)(147,242)(148,240)(149,241)(150,239)(151,238)(152,236)(153,237)(154,235)(155,234)(156,232)(157,233)(158,231)(159,230)(160,228)(161,229)(162,227)(163,206)(164,204)(165,205)(166,203)(167,222)(168,220)(169,221)(170,219)(171,218)(172,216)(173,217)(174,215)(175,214)(176,212)(177,213)(178,211)(179,210)(180,208)(181,209)(182,207); s4 := Sym(242)!( 3,127)( 4,128)( 5,129)( 6,130)( 7,123)( 8,124)( 9,125)( 10,126)( 11,139)( 12,140)( 13,141)( 14,142)( 15,135)( 16,136)( 17,137)( 18,138)( 19,131)( 20,132)( 21,133)( 22,134)( 23,147)( 24,148)( 25,149)( 26,150)( 27,143)( 28,144)( 29,145)( 30,146)( 31,159)( 32,160)( 33,161)( 34,162)( 35,155)( 36,156)( 37,157)( 38,158)( 39,151)( 40,152)( 41,153)( 42,154)( 43,167)( 44,168)( 45,169)( 46,170)( 47,163)( 48,164)( 49,165)( 50,166)( 51,179)( 52,180)( 53,181)( 54,182)( 55,175)( 56,176)( 57,177)( 58,178)( 59,171)( 60,172)( 61,173)( 62,174)( 63,187)( 64,188)( 65,189)( 66,190)( 67,183)( 68,184)( 69,185)( 70,186)( 71,199)( 72,200)( 73,201)( 74,202)( 75,195)( 76,196)( 77,197)( 78,198)( 79,191)( 80,192)( 81,193)( 82,194)( 83,207)( 84,208)( 85,209)( 86,210)( 87,203)( 88,204)( 89,205)( 90,206)( 91,219)( 92,220)( 93,221)( 94,222)( 95,215)( 96,216)( 97,217)( 98,218)( 99,211)(100,212)(101,213)(102,214)(103,227)(104,228)(105,229)(106,230)(107,223)(108,224)(109,225)(110,226)(111,239)(112,240)(113,241)(114,242)(115,235)(116,236)(117,237)(118,238)(119,231)(120,232)(121,233)(122,234); poly := sub<Sym(242)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;