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Polytope of Type {4,30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30,4}*960a
Also Known As : {{4,30|2},{30,4|2}}. if this polytope has another name.
Group : SmallGroup(960,10544)
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
   Orientable
   Flat
   Self-Dual
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 : {2,30,4}*480a, {4,30,2}*480a
   3-fold quotients : {4,10,4}*320
   4-fold quotients : {2,30,2}*240
   5-fold quotients : {4,6,4}*192a
   6-fold quotients : {2,10,4}*160, {4,10,2}*160
   8-fold quotients : {2,15,2}*120
   10-fold quotients : {2,6,4}*96a, {4,6,2}*96a
   12-fold quotients : {2,10,2}*80
   15-fold quotients : {4,2,4}*64
   20-fold quotients : {2,6,2}*48
   24-fold quotients : {2,5,2}*40
   30-fold quotients : {2,2,4}*32, {4,2,2}*32
   40-fold quotients : {2,3,2}*24
   60-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,60,4}*1920a, {4,30,8}*1920a, {8,30,4}*1920a
Permutation Representation (GAP) :
s0 := (121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)
(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)(135,165)(136,166)
(137,167)(138,168)(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)
(145,175)(146,176)(147,177)(148,178)(149,179)(150,180)(181,211)(182,212)
(183,213)(184,214)(185,215)(186,216)(187,217)(188,218)(189,219)(190,220)
(191,221)(192,222)(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)
(199,229)(200,230)(201,231)(202,232)(203,233)(204,234)(205,235)(206,236)
(207,237)(208,238)(209,239)(210,240);;
s1 := (  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,131)(  7,135)(  8,134)
(  9,133)( 10,132)( 11,126)( 12,130)( 13,129)( 14,128)( 15,127)( 16,136)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,146)( 22,150)( 23,149)( 24,148)
( 25,147)( 26,141)( 27,145)( 28,144)( 29,143)( 30,142)( 31,151)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,161)( 37,165)( 38,164)( 39,163)( 40,162)
( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,166)( 47,170)( 48,169)
( 49,168)( 50,167)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)( 56,171)
( 57,175)( 58,174)( 59,173)( 60,172)( 61,211)( 62,215)( 63,214)( 64,213)
( 65,212)( 66,221)( 67,225)( 68,224)( 69,223)( 70,222)( 71,216)( 72,220)
( 73,219)( 74,218)( 75,217)( 76,226)( 77,230)( 78,229)( 79,228)( 80,227)
( 81,236)( 82,240)( 83,239)( 84,238)( 85,237)( 86,231)( 87,235)( 88,234)
( 89,233)( 90,232)( 91,181)( 92,185)( 93,184)( 94,183)( 95,182)( 96,191)
( 97,195)( 98,194)( 99,193)(100,192)(101,186)(102,190)(103,189)(104,188)
(105,187)(106,196)(107,200)(108,199)(109,198)(110,197)(111,206)(112,210)
(113,209)(114,208)(115,207)(116,201)(117,205)(118,204)(119,203)(120,202);;
s2 := (  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)( 16, 22)
( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)( 32, 36)
( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)( 48, 55)
( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61,112)( 62,111)( 63,115)( 64,114)
( 65,113)( 66,107)( 67,106)( 68,110)( 69,109)( 70,108)( 71,117)( 72,116)
( 73,120)( 74,119)( 75,118)( 76, 97)( 77, 96)( 78,100)( 79, 99)( 80, 98)
( 81, 92)( 82, 91)( 83, 95)( 84, 94)( 85, 93)( 86,102)( 87,101)( 88,105)
( 89,104)( 90,103)(121,127)(122,126)(123,130)(124,129)(125,128)(131,132)
(133,135)(136,142)(137,141)(138,145)(139,144)(140,143)(146,147)(148,150)
(151,157)(152,156)(153,160)(154,159)(155,158)(161,162)(163,165)(166,172)
(167,171)(168,175)(169,174)(170,173)(176,177)(178,180)(181,232)(182,231)
(183,235)(184,234)(185,233)(186,227)(187,226)(188,230)(189,229)(190,228)
(191,237)(192,236)(193,240)(194,239)(195,238)(196,217)(197,216)(198,220)
(199,219)(200,218)(201,212)(202,211)(203,215)(204,214)(205,213)(206,222)
(207,221)(208,225)(209,224)(210,223);;
s3 := (  1, 61)(  2, 62)(  3, 63)(  4, 64)(  5, 65)(  6, 66)(  7, 67)(  8, 68)
(  9, 69)( 10, 70)( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)( 16, 76)
( 17, 77)( 18, 78)( 19, 79)( 20, 80)( 21, 81)( 22, 82)( 23, 83)( 24, 84)
( 25, 85)( 26, 86)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 91)( 32, 92)
( 33, 93)( 34, 94)( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 99)( 40,100)
( 41,101)( 42,102)( 43,103)( 44,104)( 45,105)( 46,106)( 47,107)( 48,108)
( 49,109)( 50,110)( 51,111)( 52,112)( 53,113)( 54,114)( 55,115)( 56,116)
( 57,117)( 58,118)( 59,119)( 60,120)(121,211)(122,212)(123,213)(124,214)
(125,215)(126,216)(127,217)(128,218)(129,219)(130,220)(131,221)(132,222)
(133,223)(134,224)(135,225)(136,226)(137,227)(138,228)(139,229)(140,230)
(141,231)(142,232)(143,233)(144,234)(145,235)(146,236)(147,237)(148,238)
(149,239)(150,240)(151,181)(152,182)(153,183)(154,184)(155,185)(156,186)
(157,187)(158,188)(159,189)(160,190)(161,191)(162,192)(163,193)(164,194)
(165,195)(166,196)(167,197)(168,198)(169,199)(170,200)(171,201)(172,202)
(173,203)(174,204)(175,205)(176,206)(177,207)(178,208)(179,209)(180,210);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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)!(121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,157)
(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)(135,165)
(136,166)(137,167)(138,168)(139,169)(140,170)(141,171)(142,172)(143,173)
(144,174)(145,175)(146,176)(147,177)(148,178)(149,179)(150,180)(181,211)
(182,212)(183,213)(184,214)(185,215)(186,216)(187,217)(188,218)(189,219)
(190,220)(191,221)(192,222)(193,223)(194,224)(195,225)(196,226)(197,227)
(198,228)(199,229)(200,230)(201,231)(202,232)(203,233)(204,234)(205,235)
(206,236)(207,237)(208,238)(209,239)(210,240);
s1 := Sym(240)!(  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,131)(  7,135)
(  8,134)(  9,133)( 10,132)( 11,126)( 12,130)( 13,129)( 14,128)( 15,127)
( 16,136)( 17,140)( 18,139)( 19,138)( 20,137)( 21,146)( 22,150)( 23,149)
( 24,148)( 25,147)( 26,141)( 27,145)( 28,144)( 29,143)( 30,142)( 31,151)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,161)( 37,165)( 38,164)( 39,163)
( 40,162)( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,166)( 47,170)
( 48,169)( 49,168)( 50,167)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)
( 56,171)( 57,175)( 58,174)( 59,173)( 60,172)( 61,211)( 62,215)( 63,214)
( 64,213)( 65,212)( 66,221)( 67,225)( 68,224)( 69,223)( 70,222)( 71,216)
( 72,220)( 73,219)( 74,218)( 75,217)( 76,226)( 77,230)( 78,229)( 79,228)
( 80,227)( 81,236)( 82,240)( 83,239)( 84,238)( 85,237)( 86,231)( 87,235)
( 88,234)( 89,233)( 90,232)( 91,181)( 92,185)( 93,184)( 94,183)( 95,182)
( 96,191)( 97,195)( 98,194)( 99,193)(100,192)(101,186)(102,190)(103,189)
(104,188)(105,187)(106,196)(107,200)(108,199)(109,198)(110,197)(111,206)
(112,210)(113,209)(114,208)(115,207)(116,201)(117,205)(118,204)(119,203)
(120,202);
s2 := Sym(240)!(  1,  7)(  2,  6)(  3, 10)(  4,  9)(  5,  8)( 11, 12)( 13, 15)
( 16, 22)( 17, 21)( 18, 25)( 19, 24)( 20, 23)( 26, 27)( 28, 30)( 31, 37)
( 32, 36)( 33, 40)( 34, 39)( 35, 38)( 41, 42)( 43, 45)( 46, 52)( 47, 51)
( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61,112)( 62,111)( 63,115)
( 64,114)( 65,113)( 66,107)( 67,106)( 68,110)( 69,109)( 70,108)( 71,117)
( 72,116)( 73,120)( 74,119)( 75,118)( 76, 97)( 77, 96)( 78,100)( 79, 99)
( 80, 98)( 81, 92)( 82, 91)( 83, 95)( 84, 94)( 85, 93)( 86,102)( 87,101)
( 88,105)( 89,104)( 90,103)(121,127)(122,126)(123,130)(124,129)(125,128)
(131,132)(133,135)(136,142)(137,141)(138,145)(139,144)(140,143)(146,147)
(148,150)(151,157)(152,156)(153,160)(154,159)(155,158)(161,162)(163,165)
(166,172)(167,171)(168,175)(169,174)(170,173)(176,177)(178,180)(181,232)
(182,231)(183,235)(184,234)(185,233)(186,227)(187,226)(188,230)(189,229)
(190,228)(191,237)(192,236)(193,240)(194,239)(195,238)(196,217)(197,216)
(198,220)(199,219)(200,218)(201,212)(202,211)(203,215)(204,214)(205,213)
(206,222)(207,221)(208,225)(209,224)(210,223);
s3 := Sym(240)!(  1, 61)(  2, 62)(  3, 63)(  4, 64)(  5, 65)(  6, 66)(  7, 67)
(  8, 68)(  9, 69)( 10, 70)( 11, 71)( 12, 72)( 13, 73)( 14, 74)( 15, 75)
( 16, 76)( 17, 77)( 18, 78)( 19, 79)( 20, 80)( 21, 81)( 22, 82)( 23, 83)
( 24, 84)( 25, 85)( 26, 86)( 27, 87)( 28, 88)( 29, 89)( 30, 90)( 31, 91)
( 32, 92)( 33, 93)( 34, 94)( 35, 95)( 36, 96)( 37, 97)( 38, 98)( 39, 99)
( 40,100)( 41,101)( 42,102)( 43,103)( 44,104)( 45,105)( 46,106)( 47,107)
( 48,108)( 49,109)( 50,110)( 51,111)( 52,112)( 53,113)( 54,114)( 55,115)
( 56,116)( 57,117)( 58,118)( 59,119)( 60,120)(121,211)(122,212)(123,213)
(124,214)(125,215)(126,216)(127,217)(128,218)(129,219)(130,220)(131,221)
(132,222)(133,223)(134,224)(135,225)(136,226)(137,227)(138,228)(139,229)
(140,230)(141,231)(142,232)(143,233)(144,234)(145,235)(146,236)(147,237)
(148,238)(149,239)(150,240)(151,181)(152,182)(153,183)(154,184)(155,185)
(156,186)(157,187)(158,188)(159,189)(160,190)(161,191)(162,192)(163,193)
(164,194)(165,195)(166,196)(167,197)(168,198)(169,199)(170,200)(171,201)
(172,202)(173,203)(174,204)(175,205)(176,206)(177,207)(178,208)(179,209)
(180,210);
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, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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