Polytope of Type {3,6,10,4} with group SmallGroup(1920,240151)

Overview

Group: SmallGroup(1920,240151)
Rank: 5
Schläfli Type: {3,6,10,4}
Vertices, edges, …: 4, 12, 40, 20, 4
Order of s₀s₁s₂s₃s₄: 20
Order of s₀s₁s₂s₃s₄s₃s₂s₁: 2
Also known as: {{3,6}₄,{6,10|2},{10,4|2}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{3,6,10,2}*960

5-fold

{3,6,2,4}*384

10-fold

20-fold

{3,3,2,2}*96

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)( 31, 52)( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)( 39, 60)( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)( 82,102)( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)( 90,110)( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)( 98,118)( 99,120)(100,119)(123,124)(127,128)(131,132)(135,136)(139,140)(141,161)(142,162)(143,164)(144,163)(145,165)(146,166)(147,168)(148,167)(149,169)(150,170)(151,172)(152,171)(153,173)(154,174)(155,176)(156,175)(157,177)(158,178)(159,180)(160,179)(183,184)(187,188)(191,192)(195,196)(199,200)(201,221)(202,222)(203,224)(204,223)(205,225)(206,226)(207,228)(208,227)(209,229)(210,230)(211,232)(212,231)(213,233)(214,234)(215,236)(216,235)(217,237)(218,238)(219,240)(220,239);;
s1 := (  1, 21)(  2, 24)(  3, 23)(  4, 22)(  5, 25)(  6, 28)(  7, 27)(  8, 26)(  9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)( 54, 56)( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)( 67, 87)( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)(110,112)(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)(126,148)(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)(134,156)(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)(166,168)(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)(185,205)(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)(193,213)(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)(222,224)(226,228)(230,232)(234,236)(238,240);;
s2 := (  1,  2)(  5, 18)(  6, 17)(  7, 19)(  8, 20)(  9, 14)( 10, 13)( 11, 15)( 12, 16)( 21, 42)( 22, 41)( 23, 43)( 24, 44)( 25, 58)( 26, 57)( 27, 59)( 28, 60)( 29, 54)( 30, 53)( 31, 55)( 32, 56)( 33, 50)( 34, 49)( 35, 51)( 36, 52)( 37, 46)( 38, 45)( 39, 47)( 40, 48)( 61, 62)( 65, 78)( 66, 77)( 67, 79)( 68, 80)( 69, 74)( 70, 73)( 71, 75)( 72, 76)( 81,102)( 82,101)( 83,103)( 84,104)( 85,118)( 86,117)( 87,119)( 88,120)( 89,114)( 90,113)( 91,115)( 92,116)( 93,110)( 94,109)( 95,111)( 96,112)( 97,106)( 98,105)( 99,107)(100,108)(121,122)(125,138)(126,137)(127,139)(128,140)(129,134)(130,133)(131,135)(132,136)(141,162)(142,161)(143,163)(144,164)(145,178)(146,177)(147,179)(148,180)(149,174)(150,173)(151,175)(152,176)(153,170)(154,169)(155,171)(156,172)(157,166)(158,165)(159,167)(160,168)(181,182)(185,198)(186,197)(187,199)(188,200)(189,194)(190,193)(191,195)(192,196)(201,222)(202,221)(203,223)(204,224)(205,238)(206,237)(207,239)(208,240)(209,234)(210,233)(211,235)(212,236)(213,230)(214,229)(215,231)(216,232)(217,226)(218,225)(219,227)(220,228);;
s3 := (  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9, 17)( 10, 18)( 11, 19)( 12, 20)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 29, 37)( 30, 38)( 31, 39)( 32, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 61, 65)( 62, 66)( 63, 67)( 64, 68)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 97)( 90, 98)( 91, 99)( 92,100)(101,105)(102,106)(103,107)(104,108)(109,117)(110,118)(111,119)(112,120)(121,185)(122,186)(123,187)(124,188)(125,181)(126,182)(127,183)(128,184)(129,197)(130,198)(131,199)(132,200)(133,193)(134,194)(135,195)(136,196)(137,189)(138,190)(139,191)(140,192)(141,205)(142,206)(143,207)(144,208)(145,201)(146,202)(147,203)(148,204)(149,217)(150,218)(151,219)(152,220)(153,213)(154,214)(155,215)(156,216)(157,209)(158,210)(159,211)(160,212)(161,225)(162,226)(163,227)(164,228)(165,221)(166,222)(167,223)(168,224)(169,237)(170,238)(171,239)(172,240)(173,233)(174,234)(175,235)(176,236)(177,229)(178,230)(179,231)(180,232);;
s4 := (  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,126)(  7,127)(  8,128)(  9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,208)( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,216)( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)(113,233)(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)(120,240);;
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, 
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(240)!(  3,  4)(  7,  8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)( 31, 52)( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)( 39, 60)( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)( 82,102)( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)( 90,110)( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)( 98,118)( 99,120)(100,119)(123,124)(127,128)(131,132)(135,136)(139,140)(141,161)(142,162)(143,164)(144,163)(145,165)(146,166)(147,168)(148,167)(149,169)(150,170)(151,172)(152,171)(153,173)(154,174)(155,176)(156,175)(157,177)(158,178)(159,180)(160,179)(183,184)(187,188)(191,192)(195,196)(199,200)(201,221)(202,222)(203,224)(204,223)(205,225)(206,226)(207,228)(208,227)(209,229)(210,230)(211,232)(212,231)(213,233)(214,234)(215,236)(216,235)(217,237)(218,238)(219,240)(220,239);
s1 := Sym(240)!(  1, 21)(  2, 24)(  3, 23)(  4, 22)(  5, 25)(  6, 28)(  7, 27)(  8, 26)(  9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)( 54, 56)( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)( 67, 87)( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)(110,112)(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)(126,148)(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)(134,156)(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)(166,168)(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)(185,205)(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)(193,213)(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)(222,224)(226,228)(230,232)(234,236)(238,240);
s2 := Sym(240)!(  1,  2)(  5, 18)(  6, 17)(  7, 19)(  8, 20)(  9, 14)( 10, 13)( 11, 15)( 12, 16)( 21, 42)( 22, 41)( 23, 43)( 24, 44)( 25, 58)( 26, 57)( 27, 59)( 28, 60)( 29, 54)( 30, 53)( 31, 55)( 32, 56)( 33, 50)( 34, 49)( 35, 51)( 36, 52)( 37, 46)( 38, 45)( 39, 47)( 40, 48)( 61, 62)( 65, 78)( 66, 77)( 67, 79)( 68, 80)( 69, 74)( 70, 73)( 71, 75)( 72, 76)( 81,102)( 82,101)( 83,103)( 84,104)( 85,118)( 86,117)( 87,119)( 88,120)( 89,114)( 90,113)( 91,115)( 92,116)( 93,110)( 94,109)( 95,111)( 96,112)( 97,106)( 98,105)( 99,107)(100,108)(121,122)(125,138)(126,137)(127,139)(128,140)(129,134)(130,133)(131,135)(132,136)(141,162)(142,161)(143,163)(144,164)(145,178)(146,177)(147,179)(148,180)(149,174)(150,173)(151,175)(152,176)(153,170)(154,169)(155,171)(156,172)(157,166)(158,165)(159,167)(160,168)(181,182)(185,198)(186,197)(187,199)(188,200)(189,194)(190,193)(191,195)(192,196)(201,222)(202,221)(203,223)(204,224)(205,238)(206,237)(207,239)(208,240)(209,234)(210,233)(211,235)(212,236)(213,230)(214,229)(215,231)(216,232)(217,226)(218,225)(219,227)(220,228);
s3 := Sym(240)!(  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9, 17)( 10, 18)( 11, 19)( 12, 20)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 29, 37)( 30, 38)( 31, 39)( 32, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 61, 65)( 62, 66)( 63, 67)( 64, 68)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 97)( 90, 98)( 91, 99)( 92,100)(101,105)(102,106)(103,107)(104,108)(109,117)(110,118)(111,119)(112,120)(121,185)(122,186)(123,187)(124,188)(125,181)(126,182)(127,183)(128,184)(129,197)(130,198)(131,199)(132,200)(133,193)(134,194)(135,195)(136,196)(137,189)(138,190)(139,191)(140,192)(141,205)(142,206)(143,207)(144,208)(145,201)(146,202)(147,203)(148,204)(149,217)(150,218)(151,219)(152,220)(153,213)(154,214)(155,215)(156,216)(157,209)(158,210)(159,211)(160,212)(161,225)(162,226)(163,227)(164,228)(165,221)(166,222)(167,223)(168,224)(169,237)(170,238)(171,239)(172,240)(173,233)(174,234)(175,235)(176,236)(177,229)(178,230)(179,231)(180,232);
s4 := Sym(240)!(  1,121)(  2,122)(  3,123)(  4,124)(  5,125)(  6,126)(  7,127)(  8,128)(  9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,208)( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,216)( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)(113,233)(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)(120,240);
poly := sub<Sym(240)|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, 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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

References