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Polytope of Type {30,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,8}*960c
if this polytope has a name.
Group : SmallGroup(960,11105)
Rank : 3
Schlafli Type : {30,8}
Number of vertices, edges, etc : 60, 240, 16
Order of s0s1s2 : 30
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {30,8,2} of size 1920
Vertex Figure Of :
   {2,30,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30,4}*480
   4-fold quotients : {15,4}*240, {30,4}*240b, {30,4}*240c
   5-fold quotients : {6,8}*192c
   8-fold quotients : {15,4}*120, {30,2}*120
   10-fold quotients : {6,4}*96
   16-fold quotients : {15,2}*60
   20-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   24-fold quotients : {10,2}*40
   40-fold quotients : {3,4}*24, {6,2}*24
   48-fold quotients : {5,2}*20
   80-fold quotients : {3,2}*12
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,8}*1920f, {30,8}*1920f, {60,8}*1920g
Permutation Representation (GAP) :
s0 := (  3,  6)(  4,  5)(  7,  8)(  9, 33)( 10, 34)( 11, 38)( 12, 37)( 13, 36)
( 14, 35)( 15, 40)( 16, 39)( 17, 25)( 18, 26)( 19, 30)( 20, 29)( 21, 28)
( 22, 27)( 23, 32)( 24, 31)( 41, 81)( 42, 82)( 43, 86)( 44, 85)( 45, 84)
( 46, 83)( 47, 88)( 48, 87)( 49,113)( 50,114)( 51,118)( 52,117)( 53,116)
( 54,115)( 55,120)( 56,119)( 57,105)( 58,106)( 59,110)( 60,109)( 61,108)
( 62,107)( 63,112)( 64,111)( 65, 97)( 66, 98)( 67,102)( 68,101)( 69,100)
( 70, 99)( 71,104)( 72,103)( 73, 89)( 74, 90)( 75, 94)( 76, 93)( 77, 92)
( 78, 91)( 79, 96)( 80, 95)(121,122)(123,125)(124,126)(129,154)(130,153)
(131,157)(132,158)(133,155)(134,156)(135,159)(136,160)(137,146)(138,145)
(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(161,202)(162,201)
(163,205)(164,206)(165,203)(166,204)(167,207)(168,208)(169,234)(170,233)
(171,237)(172,238)(173,235)(174,236)(175,239)(176,240)(177,226)(178,225)
(179,229)(180,230)(181,227)(182,228)(183,231)(184,232)(185,218)(186,217)
(187,221)(188,222)(189,219)(190,220)(191,223)(192,224)(193,210)(194,209)
(195,213)(196,214)(197,211)(198,212)(199,215)(200,216);;
s1 := (  1, 49)(  2, 50)(  3, 52)(  4, 51)(  5, 55)(  6, 56)(  7, 53)(  8, 54)
(  9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)( 16, 46)
( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 79)( 22, 80)( 23, 77)( 24, 78)
( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 71)( 30, 72)( 31, 69)( 32, 70)
( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)( 40, 62)
( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)
( 97,113)( 98,114)( 99,116)(100,115)(101,119)(102,120)(103,117)(104,118)
(107,108)(109,111)(110,112)(121,169)(122,170)(123,172)(124,171)(125,175)
(126,176)(127,173)(128,174)(129,161)(130,162)(131,164)(132,163)(133,167)
(134,168)(135,165)(136,166)(137,193)(138,194)(139,196)(140,195)(141,199)
(142,200)(143,197)(144,198)(145,185)(146,186)(147,188)(148,187)(149,191)
(150,192)(151,189)(152,190)(153,177)(154,178)(155,180)(156,179)(157,183)
(158,184)(159,181)(160,182)(201,209)(202,210)(203,212)(204,211)(205,215)
(206,216)(207,213)(208,214)(217,233)(218,234)(219,236)(220,235)(221,239)
(222,240)(223,237)(224,238)(227,228)(229,231)(230,232);;
s2 := (  1,127)(  2,128)(  3,125)(  4,126)(  5,124)(  6,123)(  7,122)(  8,121)
(  9,135)( 10,136)( 11,133)( 12,134)( 13,132)( 14,131)( 15,130)( 16,129)
( 17,143)( 18,144)( 19,141)( 20,142)( 21,140)( 22,139)( 23,138)( 24,137)
( 25,151)( 26,152)( 27,149)( 28,150)( 29,148)( 30,147)( 31,146)( 32,145)
( 33,159)( 34,160)( 35,157)( 36,158)( 37,156)( 38,155)( 39,154)( 40,153)
( 41,167)( 42,168)( 43,165)( 44,166)( 45,164)( 46,163)( 47,162)( 48,161)
( 49,175)( 50,176)( 51,173)( 52,174)( 53,172)( 54,171)( 55,170)( 56,169)
( 57,183)( 58,184)( 59,181)( 60,182)( 61,180)( 62,179)( 63,178)( 64,177)
( 65,191)( 66,192)( 67,189)( 68,190)( 69,188)( 70,187)( 71,186)( 72,185)
( 73,199)( 74,200)( 75,197)( 76,198)( 77,196)( 78,195)( 79,194)( 80,193)
( 81,207)( 82,208)( 83,205)( 84,206)( 85,204)( 86,203)( 87,202)( 88,201)
( 89,215)( 90,216)( 91,213)( 92,214)( 93,212)( 94,211)( 95,210)( 96,209)
( 97,223)( 98,224)( 99,221)(100,222)(101,220)(102,219)(103,218)(104,217)
(105,231)(106,232)(107,229)(108,230)(109,228)(110,227)(111,226)(112,225)
(113,239)(114,240)(115,237)(116,238)(117,236)(118,235)(119,234)(120,233);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(240)!(  3,  6)(  4,  5)(  7,  8)(  9, 33)( 10, 34)( 11, 38)( 12, 37)
( 13, 36)( 14, 35)( 15, 40)( 16, 39)( 17, 25)( 18, 26)( 19, 30)( 20, 29)
( 21, 28)( 22, 27)( 23, 32)( 24, 31)( 41, 81)( 42, 82)( 43, 86)( 44, 85)
( 45, 84)( 46, 83)( 47, 88)( 48, 87)( 49,113)( 50,114)( 51,118)( 52,117)
( 53,116)( 54,115)( 55,120)( 56,119)( 57,105)( 58,106)( 59,110)( 60,109)
( 61,108)( 62,107)( 63,112)( 64,111)( 65, 97)( 66, 98)( 67,102)( 68,101)
( 69,100)( 70, 99)( 71,104)( 72,103)( 73, 89)( 74, 90)( 75, 94)( 76, 93)
( 77, 92)( 78, 91)( 79, 96)( 80, 95)(121,122)(123,125)(124,126)(129,154)
(130,153)(131,157)(132,158)(133,155)(134,156)(135,159)(136,160)(137,146)
(138,145)(139,149)(140,150)(141,147)(142,148)(143,151)(144,152)(161,202)
(162,201)(163,205)(164,206)(165,203)(166,204)(167,207)(168,208)(169,234)
(170,233)(171,237)(172,238)(173,235)(174,236)(175,239)(176,240)(177,226)
(178,225)(179,229)(180,230)(181,227)(182,228)(183,231)(184,232)(185,218)
(186,217)(187,221)(188,222)(189,219)(190,220)(191,223)(192,224)(193,210)
(194,209)(195,213)(196,214)(197,211)(198,212)(199,215)(200,216);
s1 := Sym(240)!(  1, 49)(  2, 50)(  3, 52)(  4, 51)(  5, 55)(  6, 56)(  7, 53)
(  8, 54)(  9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)
( 16, 46)( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 79)( 22, 80)( 23, 77)
( 24, 78)( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 71)( 30, 72)( 31, 69)
( 32, 70)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)
( 40, 62)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)
( 88, 94)( 97,113)( 98,114)( 99,116)(100,115)(101,119)(102,120)(103,117)
(104,118)(107,108)(109,111)(110,112)(121,169)(122,170)(123,172)(124,171)
(125,175)(126,176)(127,173)(128,174)(129,161)(130,162)(131,164)(132,163)
(133,167)(134,168)(135,165)(136,166)(137,193)(138,194)(139,196)(140,195)
(141,199)(142,200)(143,197)(144,198)(145,185)(146,186)(147,188)(148,187)
(149,191)(150,192)(151,189)(152,190)(153,177)(154,178)(155,180)(156,179)
(157,183)(158,184)(159,181)(160,182)(201,209)(202,210)(203,212)(204,211)
(205,215)(206,216)(207,213)(208,214)(217,233)(218,234)(219,236)(220,235)
(221,239)(222,240)(223,237)(224,238)(227,228)(229,231)(230,232);
s2 := Sym(240)!(  1,127)(  2,128)(  3,125)(  4,126)(  5,124)(  6,123)(  7,122)
(  8,121)(  9,135)( 10,136)( 11,133)( 12,134)( 13,132)( 14,131)( 15,130)
( 16,129)( 17,143)( 18,144)( 19,141)( 20,142)( 21,140)( 22,139)( 23,138)
( 24,137)( 25,151)( 26,152)( 27,149)( 28,150)( 29,148)( 30,147)( 31,146)
( 32,145)( 33,159)( 34,160)( 35,157)( 36,158)( 37,156)( 38,155)( 39,154)
( 40,153)( 41,167)( 42,168)( 43,165)( 44,166)( 45,164)( 46,163)( 47,162)
( 48,161)( 49,175)( 50,176)( 51,173)( 52,174)( 53,172)( 54,171)( 55,170)
( 56,169)( 57,183)( 58,184)( 59,181)( 60,182)( 61,180)( 62,179)( 63,178)
( 64,177)( 65,191)( 66,192)( 67,189)( 68,190)( 69,188)( 70,187)( 71,186)
( 72,185)( 73,199)( 74,200)( 75,197)( 76,198)( 77,196)( 78,195)( 79,194)
( 80,193)( 81,207)( 82,208)( 83,205)( 84,206)( 85,204)( 86,203)( 87,202)
( 88,201)( 89,215)( 90,216)( 91,213)( 92,214)( 93,212)( 94,211)( 95,210)
( 96,209)( 97,223)( 98,224)( 99,221)(100,222)(101,220)(102,219)(103,218)
(104,217)(105,231)(106,232)(107,229)(108,230)(109,228)(110,227)(111,226)
(112,225)(113,239)(114,240)(115,237)(116,238)(117,236)(118,235)(119,234)
(120,233);
poly := sub<Sym(240)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope