Polytope of Type {2,4,6,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,10}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 5
Schlafli Type : {2,4,6,10}
Number of vertices, edges, etc : 2, 8, 24, 60, 10
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,6,10}*960b
4-fold quotients : {2,2,6,10}*480
5-fold quotients : {2,4,6,2}*384
10-fold quotients : {2,4,3,2}*192, {2,4,6,2}*192b, {2,4,6,2}*192c
12-fold quotients : {2,2,2,10}*160
20-fold quotients : {2,4,3,2}*96, {2,2,6,2}*96
24-fold quotients : {2,2,2,5}*80
40-fold quotients : {2,2,3,2}*48
60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,125)( 4,126)( 5,123)( 6,124)( 7,129)( 8,130)( 9,127)( 10,128)
( 11,133)( 12,134)( 13,131)( 14,132)( 15,137)( 16,138)( 17,135)( 18,136)
( 19,141)( 20,142)( 21,139)( 22,140)( 23,145)( 24,146)( 25,143)( 26,144)
( 27,149)( 28,150)( 29,147)( 30,148)( 31,153)( 32,154)( 33,151)( 34,152)
( 35,157)( 36,158)( 37,155)( 38,156)( 39,161)( 40,162)( 41,159)( 42,160)
( 43,165)( 44,166)( 45,163)( 46,164)( 47,169)( 48,170)( 49,167)( 50,168)
( 51,173)( 52,174)( 53,171)( 54,172)( 55,177)( 56,178)( 57,175)( 58,176)
( 59,181)( 60,182)( 61,179)( 62,180)( 63,185)( 64,186)( 65,183)( 66,184)
( 67,189)( 68,190)( 69,187)( 70,188)( 71,193)( 72,194)( 73,191)( 74,192)
( 75,197)( 76,198)( 77,195)( 78,196)( 79,201)( 80,202)( 81,199)( 82,200)
( 83,205)( 84,206)( 85,203)( 86,204)( 87,209)( 88,210)( 89,207)( 90,208)
( 91,213)( 92,214)( 93,211)( 94,212)( 95,217)( 96,218)( 97,215)( 98,216)
( 99,221)(100,222)(101,219)(102,220)(103,225)(104,226)(105,223)(106,224)
(107,229)(108,230)(109,227)(110,228)(111,233)(112,234)(113,231)(114,232)
(115,237)(116,238)(117,235)(118,236)(119,241)(120,242)(121,239)(122,240);;
s2 := ( 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);;
s3 := ( 3, 43)( 4, 46)( 5, 45)( 6, 44)( 7, 59)( 8, 62)( 9, 61)( 10, 60)
( 11, 55)( 12, 58)( 13, 57)( 14, 56)( 15, 51)( 16, 54)( 17, 53)( 18, 52)
( 19, 47)( 20, 50)( 21, 49)( 22, 48)( 24, 26)( 27, 39)( 28, 42)( 29, 41)
( 30, 40)( 31, 35)( 32, 38)( 33, 37)( 34, 36)( 63,103)( 64,106)( 65,105)
( 66,104)( 67,119)( 68,122)( 69,121)( 70,120)( 71,115)( 72,118)( 73,117)
( 74,116)( 75,111)( 76,114)( 77,113)( 78,112)( 79,107)( 80,110)( 81,109)
( 82,108)( 84, 86)( 87, 99)( 88,102)( 89,101)( 90,100)( 91, 95)( 92, 98)
( 93, 97)( 94, 96)(123,163)(124,166)(125,165)(126,164)(127,179)(128,182)
(129,181)(130,180)(131,175)(132,178)(133,177)(134,176)(135,171)(136,174)
(137,173)(138,172)(139,167)(140,170)(141,169)(142,168)(144,146)(147,159)
(148,162)(149,161)(150,160)(151,155)(152,158)(153,157)(154,156)(183,223)
(184,226)(185,225)(186,224)(187,239)(188,242)(189,241)(190,240)(191,235)
(192,238)(193,237)(194,236)(195,231)(196,234)(197,233)(198,232)(199,227)
(200,230)(201,229)(202,228)(204,206)(207,219)(208,222)(209,221)(210,220)
(211,215)(212,218)(213,217)(214,216);;
s4 := ( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 63)( 8, 64)( 9, 65)( 10, 66)
( 11, 79)( 12, 80)( 13, 81)( 14, 82)( 15, 75)( 16, 76)( 17, 77)( 18, 78)
( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 87)( 24, 88)( 25, 89)( 26, 90)
( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 99)( 32,100)( 33,101)( 34,102)
( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 91)( 40, 92)( 41, 93)( 42, 94)
( 43,107)( 44,108)( 45,109)( 46,110)( 47,103)( 48,104)( 49,105)( 50,106)
( 51,119)( 52,120)( 53,121)( 54,122)( 55,115)( 56,116)( 57,117)( 58,118)
( 59,111)( 60,112)( 61,113)( 62,114)(123,187)(124,188)(125,189)(126,190)
(127,183)(128,184)(129,185)(130,186)(131,199)(132,200)(133,201)(134,202)
(135,195)(136,196)(137,197)(138,198)(139,191)(140,192)(141,193)(142,194)
(143,207)(144,208)(145,209)(146,210)(147,203)(148,204)(149,205)(150,206)
(151,219)(152,220)(153,221)(154,222)(155,215)(156,216)(157,217)(158,218)
(159,211)(160,212)(161,213)(162,214)(163,227)(164,228)(165,229)(166,230)
(167,223)(168,224)(169,225)(170,226)(171,239)(172,240)(173,241)(174,242)
(175,235)(176,236)(177,237)(178,238)(179,231)(180,232)(181,233)(182,234);;
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*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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)!( 3,125)( 4,126)( 5,123)( 6,124)( 7,129)( 8,130)( 9,127)
( 10,128)( 11,133)( 12,134)( 13,131)( 14,132)( 15,137)( 16,138)( 17,135)
( 18,136)( 19,141)( 20,142)( 21,139)( 22,140)( 23,145)( 24,146)( 25,143)
( 26,144)( 27,149)( 28,150)( 29,147)( 30,148)( 31,153)( 32,154)( 33,151)
( 34,152)( 35,157)( 36,158)( 37,155)( 38,156)( 39,161)( 40,162)( 41,159)
( 42,160)( 43,165)( 44,166)( 45,163)( 46,164)( 47,169)( 48,170)( 49,167)
( 50,168)( 51,173)( 52,174)( 53,171)( 54,172)( 55,177)( 56,178)( 57,175)
( 58,176)( 59,181)( 60,182)( 61,179)( 62,180)( 63,185)( 64,186)( 65,183)
( 66,184)( 67,189)( 68,190)( 69,187)( 70,188)( 71,193)( 72,194)( 73,191)
( 74,192)( 75,197)( 76,198)( 77,195)( 78,196)( 79,201)( 80,202)( 81,199)
( 82,200)( 83,205)( 84,206)( 85,203)( 86,204)( 87,209)( 88,210)( 89,207)
( 90,208)( 91,213)( 92,214)( 93,211)( 94,212)( 95,217)( 96,218)( 97,215)
( 98,216)( 99,221)(100,222)(101,219)(102,220)(103,225)(104,226)(105,223)
(106,224)(107,229)(108,230)(109,227)(110,228)(111,233)(112,234)(113,231)
(114,232)(115,237)(116,238)(117,235)(118,236)(119,241)(120,242)(121,239)
(122,240);
s2 := 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);
s3 := Sym(242)!( 3, 43)( 4, 46)( 5, 45)( 6, 44)( 7, 59)( 8, 62)( 9, 61)
( 10, 60)( 11, 55)( 12, 58)( 13, 57)( 14, 56)( 15, 51)( 16, 54)( 17, 53)
( 18, 52)( 19, 47)( 20, 50)( 21, 49)( 22, 48)( 24, 26)( 27, 39)( 28, 42)
( 29, 41)( 30, 40)( 31, 35)( 32, 38)( 33, 37)( 34, 36)( 63,103)( 64,106)
( 65,105)( 66,104)( 67,119)( 68,122)( 69,121)( 70,120)( 71,115)( 72,118)
( 73,117)( 74,116)( 75,111)( 76,114)( 77,113)( 78,112)( 79,107)( 80,110)
( 81,109)( 82,108)( 84, 86)( 87, 99)( 88,102)( 89,101)( 90,100)( 91, 95)
( 92, 98)( 93, 97)( 94, 96)(123,163)(124,166)(125,165)(126,164)(127,179)
(128,182)(129,181)(130,180)(131,175)(132,178)(133,177)(134,176)(135,171)
(136,174)(137,173)(138,172)(139,167)(140,170)(141,169)(142,168)(144,146)
(147,159)(148,162)(149,161)(150,160)(151,155)(152,158)(153,157)(154,156)
(183,223)(184,226)(185,225)(186,224)(187,239)(188,242)(189,241)(190,240)
(191,235)(192,238)(193,237)(194,236)(195,231)(196,234)(197,233)(198,232)
(199,227)(200,230)(201,229)(202,228)(204,206)(207,219)(208,222)(209,221)
(210,220)(211,215)(212,218)(213,217)(214,216);
s4 := Sym(242)!( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 63)( 8, 64)( 9, 65)
( 10, 66)( 11, 79)( 12, 80)( 13, 81)( 14, 82)( 15, 75)( 16, 76)( 17, 77)
( 18, 78)( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 87)( 24, 88)( 25, 89)
( 26, 90)( 27, 83)( 28, 84)( 29, 85)( 30, 86)( 31, 99)( 32,100)( 33,101)
( 34,102)( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 91)( 40, 92)( 41, 93)
( 42, 94)( 43,107)( 44,108)( 45,109)( 46,110)( 47,103)( 48,104)( 49,105)
( 50,106)( 51,119)( 52,120)( 53,121)( 54,122)( 55,115)( 56,116)( 57,117)
( 58,118)( 59,111)( 60,112)( 61,113)( 62,114)(123,187)(124,188)(125,189)
(126,190)(127,183)(128,184)(129,185)(130,186)(131,199)(132,200)(133,201)
(134,202)(135,195)(136,196)(137,197)(138,198)(139,191)(140,192)(141,193)
(142,194)(143,207)(144,208)(145,209)(146,210)(147,203)(148,204)(149,205)
(150,206)(151,219)(152,220)(153,221)(154,222)(155,215)(156,216)(157,217)
(158,218)(159,211)(160,212)(161,213)(162,214)(163,227)(164,228)(165,229)
(166,230)(167,223)(168,224)(169,225)(170,226)(171,239)(172,240)(173,241)
(174,242)(175,235)(176,236)(177,237)(178,238)(179,231)(180,232)(181,233)
(182,234);
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*s1*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope