Overview
- Group
- SmallGroup(1920,240213)
- Rank
- 4
- Schläfli Type
- {6,6,10}
- Vertices, edges, …
- 16, 48, 80, 10
- Order of s0s1s2s3
- 40
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
5-fold
10-fold
20-fold
24-fold
40-fold
48-fold
120-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<(s0*s1)^3> of order 2
10 facets
- 10 of 2-fold non-regular quotient of {6,6}*192b
8 vertex figures
- 8 of {6,10}*120
P/N, where N=<(s0*s1)^2> of order 3
10 facets
- 10 of 3-fold non-regular quotient of {6,6}*192b
8 vertex figures
- 4 of {6,10}*120
- 4 of {2,10}*40
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)( 65,105)( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)( 73,113)( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)(121,122)(125,128)(126,127)(129,130)(133,136)(134,135)(137,138)(141,144)(142,143)(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)(161,202)(162,201)(163,203)(164,204)(165,208)(166,207)(167,206)(168,205)(169,210)(170,209)(171,211)(172,212)(173,216)(174,215)(175,214)(176,213)(177,218)(178,217)(179,219)(180,220)(181,224)(182,223)(183,222)(184,221)(185,226)(186,225)(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,234)(194,233)(195,235)(196,236)(197,240)(198,239)(199,238)(200,237);; s1 := ( 1, 41)( 2, 42)( 3, 47)( 4, 48)( 5, 46)( 6, 45)( 7, 43)( 8, 44)( 9, 49)( 10, 50)( 11, 55)( 12, 56)( 13, 54)( 14, 53)( 15, 51)( 16, 52)( 17, 57)( 18, 58)( 19, 63)( 20, 64)( 21, 62)( 22, 61)( 23, 59)( 24, 60)( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)( 32, 68)( 33, 73)( 34, 74)( 35, 79)( 36, 80)( 37, 78)( 38, 77)( 39, 75)( 40, 76)( 83, 87)( 84, 88)( 85, 86)( 91, 95)( 92, 96)( 93, 94)( 99,103)(100,104)(101,102)(107,111)(108,112)(109,110)(115,119)(116,120)(117,118)(121,161)(122,162)(123,167)(124,168)(125,166)(126,165)(127,163)(128,164)(129,169)(130,170)(131,175)(132,176)(133,174)(134,173)(135,171)(136,172)(137,177)(138,178)(139,183)(140,184)(141,182)(142,181)(143,179)(144,180)(145,185)(146,186)(147,191)(148,192)(149,190)(150,189)(151,187)(152,188)(153,193)(154,194)(155,199)(156,200)(157,198)(158,197)(159,195)(160,196)(203,207)(204,208)(205,206)(211,215)(212,216)(213,214)(219,223)(220,224)(221,222)(227,231)(228,232)(229,230)(235,239)(236,240)(237,238);; s2 := ( 1,123)( 2,124)( 3,121)( 4,122)( 5,126)( 6,125)( 7,127)( 8,128)( 9,155)( 10,156)( 11,153)( 12,154)( 13,158)( 14,157)( 15,159)( 16,160)( 17,147)( 18,148)( 19,145)( 20,146)( 21,150)( 22,149)( 23,151)( 24,152)( 25,139)( 26,140)( 27,137)( 28,138)( 29,142)( 30,141)( 31,143)( 32,144)( 33,131)( 34,132)( 35,129)( 36,130)( 37,134)( 38,133)( 39,135)( 40,136)( 41,203)( 42,204)( 43,201)( 44,202)( 45,206)( 46,205)( 47,207)( 48,208)( 49,235)( 50,236)( 51,233)( 52,234)( 53,238)( 54,237)( 55,239)( 56,240)( 57,227)( 58,228)( 59,225)( 60,226)( 61,230)( 62,229)( 63,231)( 64,232)( 65,219)( 66,220)( 67,217)( 68,218)( 69,222)( 70,221)( 71,223)( 72,224)( 73,211)( 74,212)( 75,209)( 76,210)( 77,214)( 78,213)( 79,215)( 80,216)( 81,163)( 82,164)( 83,161)( 84,162)( 85,166)( 86,165)( 87,167)( 88,168)( 89,195)( 90,196)( 91,193)( 92,194)( 93,198)( 94,197)( 95,199)( 96,200)( 97,187)( 98,188)( 99,185)(100,186)(101,190)(102,189)(103,191)(104,192)(105,179)(106,180)(107,177)(108,178)(109,182)(110,181)(111,183)(112,184)(113,171)(114,172)(115,169)(116,170)(117,174)(118,173)(119,175)(120,176);; s3 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)( 24, 40)( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 57, 73)( 58, 74)( 59, 75)( 60, 76)( 61, 77)( 62, 78)( 63, 79)( 64, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 97,113)( 98,114)( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)(137,153)(138,154)(139,155)(140,156)(141,157)(142,158)(143,159)(144,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(177,193)(178,194)(179,195)(180,196)(181,197)(182,198)(183,199)(184,200)(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)(217,233)(218,234)(219,235)(220,236)(221,237)(222,238)(223,239)(224,240);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s2*s1*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)( 5, 7)( 6, 8)( 11, 12)( 13, 15)( 14, 16)( 19, 20)( 21, 23)( 22, 24)( 27, 28)( 29, 31)( 30, 32)( 35, 36)( 37, 39)( 38, 40)( 41, 81)( 42, 82)( 43, 84)( 44, 83)( 45, 87)( 46, 88)( 47, 85)( 48, 86)( 49, 89)( 50, 90)( 51, 92)( 52, 91)( 53, 95)( 54, 96)( 55, 93)( 56, 94)( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,103)( 62,104)( 63,101)( 64,102)( 65,105)( 66,106)( 67,108)( 68,107)( 69,111)( 70,112)( 71,109)( 72,110)( 73,113)( 74,114)( 75,116)( 76,115)( 77,119)( 78,120)( 79,117)( 80,118)(121,122)(125,128)(126,127)(129,130)(133,136)(134,135)(137,138)(141,144)(142,143)(145,146)(149,152)(150,151)(153,154)(157,160)(158,159)(161,202)(162,201)(163,203)(164,204)(165,208)(166,207)(167,206)(168,205)(169,210)(170,209)(171,211)(172,212)(173,216)(174,215)(175,214)(176,213)(177,218)(178,217)(179,219)(180,220)(181,224)(182,223)(183,222)(184,221)(185,226)(186,225)(187,227)(188,228)(189,232)(190,231)(191,230)(192,229)(193,234)(194,233)(195,235)(196,236)(197,240)(198,239)(199,238)(200,237); s1 := Sym(240)!( 1, 41)( 2, 42)( 3, 47)( 4, 48)( 5, 46)( 6, 45)( 7, 43)( 8, 44)( 9, 49)( 10, 50)( 11, 55)( 12, 56)( 13, 54)( 14, 53)( 15, 51)( 16, 52)( 17, 57)( 18, 58)( 19, 63)( 20, 64)( 21, 62)( 22, 61)( 23, 59)( 24, 60)( 25, 65)( 26, 66)( 27, 71)( 28, 72)( 29, 70)( 30, 69)( 31, 67)( 32, 68)( 33, 73)( 34, 74)( 35, 79)( 36, 80)( 37, 78)( 38, 77)( 39, 75)( 40, 76)( 83, 87)( 84, 88)( 85, 86)( 91, 95)( 92, 96)( 93, 94)( 99,103)(100,104)(101,102)(107,111)(108,112)(109,110)(115,119)(116,120)(117,118)(121,161)(122,162)(123,167)(124,168)(125,166)(126,165)(127,163)(128,164)(129,169)(130,170)(131,175)(132,176)(133,174)(134,173)(135,171)(136,172)(137,177)(138,178)(139,183)(140,184)(141,182)(142,181)(143,179)(144,180)(145,185)(146,186)(147,191)(148,192)(149,190)(150,189)(151,187)(152,188)(153,193)(154,194)(155,199)(156,200)(157,198)(158,197)(159,195)(160,196)(203,207)(204,208)(205,206)(211,215)(212,216)(213,214)(219,223)(220,224)(221,222)(227,231)(228,232)(229,230)(235,239)(236,240)(237,238); s2 := Sym(240)!( 1,123)( 2,124)( 3,121)( 4,122)( 5,126)( 6,125)( 7,127)( 8,128)( 9,155)( 10,156)( 11,153)( 12,154)( 13,158)( 14,157)( 15,159)( 16,160)( 17,147)( 18,148)( 19,145)( 20,146)( 21,150)( 22,149)( 23,151)( 24,152)( 25,139)( 26,140)( 27,137)( 28,138)( 29,142)( 30,141)( 31,143)( 32,144)( 33,131)( 34,132)( 35,129)( 36,130)( 37,134)( 38,133)( 39,135)( 40,136)( 41,203)( 42,204)( 43,201)( 44,202)( 45,206)( 46,205)( 47,207)( 48,208)( 49,235)( 50,236)( 51,233)( 52,234)( 53,238)( 54,237)( 55,239)( 56,240)( 57,227)( 58,228)( 59,225)( 60,226)( 61,230)( 62,229)( 63,231)( 64,232)( 65,219)( 66,220)( 67,217)( 68,218)( 69,222)( 70,221)( 71,223)( 72,224)( 73,211)( 74,212)( 75,209)( 76,210)( 77,214)( 78,213)( 79,215)( 80,216)( 81,163)( 82,164)( 83,161)( 84,162)( 85,166)( 86,165)( 87,167)( 88,168)( 89,195)( 90,196)( 91,193)( 92,194)( 93,198)( 94,197)( 95,199)( 96,200)( 97,187)( 98,188)( 99,185)(100,186)(101,190)(102,189)(103,191)(104,192)(105,179)(106,180)(107,177)(108,178)(109,182)(110,181)(111,183)(112,184)(113,171)(114,172)(115,169)(116,170)(117,174)(118,173)(119,175)(120,176); s3 := Sym(240)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 17, 33)( 18, 34)( 19, 35)( 20, 36)( 21, 37)( 22, 38)( 23, 39)( 24, 40)( 41, 49)( 42, 50)( 43, 51)( 44, 52)( 45, 53)( 46, 54)( 47, 55)( 48, 56)( 57, 73)( 58, 74)( 59, 75)( 60, 76)( 61, 77)( 62, 78)( 63, 79)( 64, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 97,113)( 98,114)( 99,115)(100,116)(101,117)(102,118)(103,119)(104,120)(121,129)(122,130)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)(137,153)(138,154)(139,155)(140,156)(141,157)(142,158)(143,159)(144,160)(161,169)(162,170)(163,171)(164,172)(165,173)(166,174)(167,175)(168,176)(177,193)(178,194)(179,195)(180,196)(181,197)(182,198)(183,199)(184,200)(201,209)(202,210)(203,211)(204,212)(205,213)(206,214)(207,215)(208,216)(217,233)(218,234)(219,235)(220,236)(221,237)(222,238)(223,239)(224,240); poly := sub<Sym(240)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s0*s1*s2*s1*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
None.
to this polytope.