Overview
- Group
- SmallGroup(1920,240409)
- Rank
- 5
- Schläfli Type
- {2,2,4,15}
- Vertices, edges, …
- 2, 2, 16, 120, 60
- Order of s0s1s2s3s4
- 30
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := ( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)( 27, 35)( 28, 36)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)( 74, 82)( 75, 83)( 76, 84)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)( 91, 99)( 92,100)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)(107,115)(108,116)(117,125)(118,126)(119,127)(120,128)(121,129)(122,130)(123,131)(124,132)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146)(139,147)(140,148)(149,157)(150,158)(151,159)(152,160)(153,161)(154,162)(155,163)(156,164)(165,173)(166,174)(167,175)(168,176)(169,177)(170,178)(171,179)(172,180)(181,189)(182,190)(183,191)(184,192)(185,193)(186,194)(187,195)(188,196)(197,205)(198,206)(199,207)(200,208)(201,209)(202,210)(203,211)(204,212)(213,221)(214,222)(215,223)(216,224)(217,225)(218,226)(219,227)(220,228)(229,237)(230,238)(231,239)(232,240)(233,241)(234,242)(235,243)(236,244);; s3 := ( 6, 15)( 7, 18)( 8, 12)( 10, 19)( 11, 14)( 13, 17)( 21, 69)( 22, 79)( 23, 82)( 24, 76)( 25, 73)( 26, 83)( 27, 78)( 28, 72)( 29, 81)( 30, 75)( 31, 70)( 32, 80)( 33, 77)( 34, 71)( 35, 74)( 36, 84)( 37, 53)( 38, 63)( 39, 66)( 40, 60)( 41, 57)( 42, 67)( 43, 62)( 44, 56)( 45, 65)( 46, 59)( 47, 54)( 48, 64)( 49, 61)( 50, 55)( 51, 58)( 52, 68)( 85,165)( 86,175)( 87,178)( 88,172)( 89,169)( 90,179)( 91,174)( 92,168)( 93,177)( 94,171)( 95,166)( 96,176)( 97,173)( 98,167)( 99,170)(100,180)(101,229)(102,239)(103,242)(104,236)(105,233)(106,243)(107,238)(108,232)(109,241)(110,235)(111,230)(112,240)(113,237)(114,231)(115,234)(116,244)(117,213)(118,223)(119,226)(120,220)(121,217)(122,227)(123,222)(124,216)(125,225)(126,219)(127,214)(128,224)(129,221)(130,215)(131,218)(132,228)(133,197)(134,207)(135,210)(136,204)(137,201)(138,211)(139,206)(140,200)(141,209)(142,203)(143,198)(144,208)(145,205)(146,199)(147,202)(148,212)(149,181)(150,191)(151,194)(152,188)(153,185)(154,195)(155,190)(156,184)(157,193)(158,187)(159,182)(160,192)(161,189)(162,183)(163,186)(164,196);; s4 := ( 5,117)( 6,129)( 7,124)( 8,128)( 9,126)( 10,122)( 11,131)( 12,119)( 13,125)( 14,121)( 15,132)( 16,120)( 17,118)( 18,130)( 19,123)( 20,127)( 21,101)( 22,113)( 23,108)( 24,112)( 25,110)( 26,106)( 27,115)( 28,103)( 29,109)( 30,105)( 31,116)( 32,104)( 33,102)( 34,114)( 35,107)( 36,111)( 37, 85)( 38, 97)( 39, 92)( 40, 96)( 41, 94)( 42, 90)( 43, 99)( 44, 87)( 45, 93)( 46, 89)( 47,100)( 48, 88)( 49, 86)( 50, 98)( 51, 91)( 52, 95)( 53,149)( 54,161)( 55,156)( 56,160)( 57,158)( 58,154)( 59,163)( 60,151)( 61,157)( 62,153)( 63,164)( 64,152)( 65,150)( 66,162)( 67,155)( 68,159)( 69,133)( 70,145)( 71,140)( 72,144)( 73,142)( 74,138)( 75,147)( 76,135)( 77,141)( 78,137)( 79,148)( 80,136)( 81,134)( 82,146)( 83,139)( 84,143)(165,197)(166,209)(167,204)(168,208)(169,206)(170,202)(171,211)(172,199)(173,205)(174,201)(175,212)(176,200)(177,198)(178,210)(179,203)(180,207)(182,193)(183,188)(184,192)(185,190)(187,195)(191,196)(213,229)(214,241)(215,236)(216,240)(217,238)(218,234)(219,243)(220,231)(221,237)(222,233)(223,244)(224,232)(225,230)(226,242)(227,235)(228,239);; 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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3,
s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3*s4*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(244)!(1,2); s1 := Sym(244)!(3,4); s2 := Sym(244)!( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)( 10, 18)( 11, 19)( 12, 20)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 25, 33)( 26, 34)( 27, 35)( 28, 36)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)( 58, 66)( 59, 67)( 60, 68)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 73, 81)( 74, 82)( 75, 83)( 76, 84)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 89, 97)( 90, 98)( 91, 99)( 92,100)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)(107,115)(108,116)(117,125)(118,126)(119,127)(120,128)(121,129)(122,130)(123,131)(124,132)(133,141)(134,142)(135,143)(136,144)(137,145)(138,146)(139,147)(140,148)(149,157)(150,158)(151,159)(152,160)(153,161)(154,162)(155,163)(156,164)(165,173)(166,174)(167,175)(168,176)(169,177)(170,178)(171,179)(172,180)(181,189)(182,190)(183,191)(184,192)(185,193)(186,194)(187,195)(188,196)(197,205)(198,206)(199,207)(200,208)(201,209)(202,210)(203,211)(204,212)(213,221)(214,222)(215,223)(216,224)(217,225)(218,226)(219,227)(220,228)(229,237)(230,238)(231,239)(232,240)(233,241)(234,242)(235,243)(236,244); s3 := Sym(244)!( 6, 15)( 7, 18)( 8, 12)( 10, 19)( 11, 14)( 13, 17)( 21, 69)( 22, 79)( 23, 82)( 24, 76)( 25, 73)( 26, 83)( 27, 78)( 28, 72)( 29, 81)( 30, 75)( 31, 70)( 32, 80)( 33, 77)( 34, 71)( 35, 74)( 36, 84)( 37, 53)( 38, 63)( 39, 66)( 40, 60)( 41, 57)( 42, 67)( 43, 62)( 44, 56)( 45, 65)( 46, 59)( 47, 54)( 48, 64)( 49, 61)( 50, 55)( 51, 58)( 52, 68)( 85,165)( 86,175)( 87,178)( 88,172)( 89,169)( 90,179)( 91,174)( 92,168)( 93,177)( 94,171)( 95,166)( 96,176)( 97,173)( 98,167)( 99,170)(100,180)(101,229)(102,239)(103,242)(104,236)(105,233)(106,243)(107,238)(108,232)(109,241)(110,235)(111,230)(112,240)(113,237)(114,231)(115,234)(116,244)(117,213)(118,223)(119,226)(120,220)(121,217)(122,227)(123,222)(124,216)(125,225)(126,219)(127,214)(128,224)(129,221)(130,215)(131,218)(132,228)(133,197)(134,207)(135,210)(136,204)(137,201)(138,211)(139,206)(140,200)(141,209)(142,203)(143,198)(144,208)(145,205)(146,199)(147,202)(148,212)(149,181)(150,191)(151,194)(152,188)(153,185)(154,195)(155,190)(156,184)(157,193)(158,187)(159,182)(160,192)(161,189)(162,183)(163,186)(164,196); s4 := Sym(244)!( 5,117)( 6,129)( 7,124)( 8,128)( 9,126)( 10,122)( 11,131)( 12,119)( 13,125)( 14,121)( 15,132)( 16,120)( 17,118)( 18,130)( 19,123)( 20,127)( 21,101)( 22,113)( 23,108)( 24,112)( 25,110)( 26,106)( 27,115)( 28,103)( 29,109)( 30,105)( 31,116)( 32,104)( 33,102)( 34,114)( 35,107)( 36,111)( 37, 85)( 38, 97)( 39, 92)( 40, 96)( 41, 94)( 42, 90)( 43, 99)( 44, 87)( 45, 93)( 46, 89)( 47,100)( 48, 88)( 49, 86)( 50, 98)( 51, 91)( 52, 95)( 53,149)( 54,161)( 55,156)( 56,160)( 57,158)( 58,154)( 59,163)( 60,151)( 61,157)( 62,153)( 63,164)( 64,152)( 65,150)( 66,162)( 67,155)( 68,159)( 69,133)( 70,145)( 71,140)( 72,144)( 73,142)( 74,138)( 75,147)( 76,135)( 77,141)( 78,137)( 79,148)( 80,136)( 81,134)( 82,146)( 83,139)( 84,143)(165,197)(166,209)(167,204)(168,208)(169,206)(170,202)(171,211)(172,199)(173,205)(174,201)(175,212)(176,200)(177,198)(178,210)(179,203)(180,207)(182,193)(183,188)(184,192)(185,190)(187,195)(191,196)(213,229)(214,241)(215,236)(216,240)(217,238)(218,234)(219,243)(220,231)(221,237)(222,233)(223,244)(224,232)(225,230)(226,242)(227,235)(228,239); poly := sub<Sym(244)|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, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3*s2*s3*s4*s3, s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s3*s2*s3*s4*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 >;