Polytope of Type {4,30,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30,4}*960c
if this polytope has a name.
Group : SmallGroup(960,11092)
Rank : 4
Schlafli Type : {4,30,4}
Number of vertices, edges, etc : 4, 60, 60, 4
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,30,4,2} of size 1920
Vertex Figure Of :
{2,4,30,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,30,2}*480b
4-fold quotients : {4,15,2}*240
5-fold quotients : {4,6,4}*192c
10-fold quotients : {4,6,2}*96c
20-fold quotients : {4,3,2}*48
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,60,4}*1920d, {4,60,4}*1920e, {4,30,8}*1920b, {4,30,4}*1920b
Permutation Representation (GAP) :
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240);;
s1 := ( 2, 3)( 5, 17)( 6, 19)( 7, 18)( 8, 20)( 9, 13)( 10, 15)( 11, 14)
( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)( 27, 58)
( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)( 35, 50)
( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)( 66, 79)
( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)( 90,115)
( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)( 98,107)
( 99,106)(100,108)(122,123)(125,137)(126,139)(127,138)(128,140)(129,133)
(130,135)(131,134)(132,136)(141,161)(142,163)(143,162)(144,164)(145,177)
(146,179)(147,178)(148,180)(149,173)(150,175)(151,174)(152,176)(153,169)
(154,171)(155,170)(156,172)(157,165)(158,167)(159,166)(160,168)(182,183)
(185,197)(186,199)(187,198)(188,200)(189,193)(190,195)(191,194)(192,196)
(201,221)(202,223)(203,222)(204,224)(205,237)(206,239)(207,238)(208,240)
(209,233)(210,235)(211,234)(212,236)(213,229)(214,231)(215,230)(216,232)
(217,225)(218,227)(219,226)(220,228);;
s2 := ( 1, 45)( 2, 48)( 3, 47)( 4, 46)( 5, 41)( 6, 44)( 7, 43)( 8, 42)
( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 53)( 14, 56)( 15, 55)( 16, 54)
( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 25)( 22, 28)( 23, 27)( 24, 26)
( 29, 37)( 30, 40)( 31, 39)( 32, 38)( 34, 36)( 61,105)( 62,108)( 63,107)
( 64,106)( 65,101)( 66,104)( 67,103)( 68,102)( 69,117)( 70,120)( 71,119)
( 72,118)( 73,113)( 74,116)( 75,115)( 76,114)( 77,109)( 78,112)( 79,111)
( 80,110)( 81, 85)( 82, 88)( 83, 87)( 84, 86)( 89, 97)( 90,100)( 91, 99)
( 92, 98)( 94, 96)(121,225)(122,228)(123,227)(124,226)(125,221)(126,224)
(127,223)(128,222)(129,237)(130,240)(131,239)(132,238)(133,233)(134,236)
(135,235)(136,234)(137,229)(138,232)(139,231)(140,230)(141,205)(142,208)
(143,207)(144,206)(145,201)(146,204)(147,203)(148,202)(149,217)(150,220)
(151,219)(152,218)(153,213)(154,216)(155,215)(156,214)(157,209)(158,212)
(159,211)(160,210)(161,185)(162,188)(163,187)(164,186)(165,181)(166,184)
(167,183)(168,182)(169,197)(170,200)(171,199)(172,198)(173,193)(174,196)
(175,195)(176,194)(177,189)(178,192)(179,191)(180,190);;
s3 := ( 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]);;
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, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(240)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240);
s1 := Sym(240)!( 2, 3)( 5, 17)( 6, 19)( 7, 18)( 8, 20)( 9, 13)( 10, 15)
( 11, 14)( 12, 16)( 21, 41)( 22, 43)( 23, 42)( 24, 44)( 25, 57)( 26, 59)
( 27, 58)( 28, 60)( 29, 53)( 30, 55)( 31, 54)( 32, 56)( 33, 49)( 34, 51)
( 35, 50)( 36, 52)( 37, 45)( 38, 47)( 39, 46)( 40, 48)( 62, 63)( 65, 77)
( 66, 79)( 67, 78)( 68, 80)( 69, 73)( 70, 75)( 71, 74)( 72, 76)( 81,101)
( 82,103)( 83,102)( 84,104)( 85,117)( 86,119)( 87,118)( 88,120)( 89,113)
( 90,115)( 91,114)( 92,116)( 93,109)( 94,111)( 95,110)( 96,112)( 97,105)
( 98,107)( 99,106)(100,108)(122,123)(125,137)(126,139)(127,138)(128,140)
(129,133)(130,135)(131,134)(132,136)(141,161)(142,163)(143,162)(144,164)
(145,177)(146,179)(147,178)(148,180)(149,173)(150,175)(151,174)(152,176)
(153,169)(154,171)(155,170)(156,172)(157,165)(158,167)(159,166)(160,168)
(182,183)(185,197)(186,199)(187,198)(188,200)(189,193)(190,195)(191,194)
(192,196)(201,221)(202,223)(203,222)(204,224)(205,237)(206,239)(207,238)
(208,240)(209,233)(210,235)(211,234)(212,236)(213,229)(214,231)(215,230)
(216,232)(217,225)(218,227)(219,226)(220,228);
s2 := Sym(240)!( 1, 45)( 2, 48)( 3, 47)( 4, 46)( 5, 41)( 6, 44)( 7, 43)
( 8, 42)( 9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 53)( 14, 56)( 15, 55)
( 16, 54)( 17, 49)( 18, 52)( 19, 51)( 20, 50)( 21, 25)( 22, 28)( 23, 27)
( 24, 26)( 29, 37)( 30, 40)( 31, 39)( 32, 38)( 34, 36)( 61,105)( 62,108)
( 63,107)( 64,106)( 65,101)( 66,104)( 67,103)( 68,102)( 69,117)( 70,120)
( 71,119)( 72,118)( 73,113)( 74,116)( 75,115)( 76,114)( 77,109)( 78,112)
( 79,111)( 80,110)( 81, 85)( 82, 88)( 83, 87)( 84, 86)( 89, 97)( 90,100)
( 91, 99)( 92, 98)( 94, 96)(121,225)(122,228)(123,227)(124,226)(125,221)
(126,224)(127,223)(128,222)(129,237)(130,240)(131,239)(132,238)(133,233)
(134,236)(135,235)(136,234)(137,229)(138,232)(139,231)(140,230)(141,205)
(142,208)(143,207)(144,206)(145,201)(146,204)(147,203)(148,202)(149,217)
(150,220)(151,219)(152,218)(153,213)(154,216)(155,215)(156,214)(157,209)
(158,212)(159,211)(160,210)(161,185)(162,188)(163,187)(164,186)(165,181)
(166,184)(167,183)(168,182)(169,197)(170,200)(171,199)(172,198)(173,193)
(174,196)(175,195)(176,194)(177,189)(178,192)(179,191)(180,190);
s3 := 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>;
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,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope