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Polytope of Type {30,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,16}*960
Also Known As : {30,16|2}. if this polytope has another name.
Group : SmallGroup(960,5206)
Rank : 3
Schlafli Type : {30,16}
Number of vertices, edges, etc : 30, 240, 16
Order of s0s1s2 : 240
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {30,16,2} of size 1920
Vertex Figure Of :
   {2,30,16} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30,8}*480
   3-fold quotients : {10,16}*320
   4-fold quotients : {30,4}*240a
   5-fold quotients : {6,16}*192
   6-fold quotients : {10,8}*160
   8-fold quotients : {30,2}*120
   10-fold quotients : {6,8}*96
   12-fold quotients : {10,4}*80
   15-fold quotients : {2,16}*64
   16-fold quotients : {15,2}*60
   20-fold quotients : {6,4}*48a
   24-fold quotients : {10,2}*40
   30-fold quotients : {2,8}*32
   40-fold quotients : {6,2}*24
   48-fold quotients : {5,2}*20
   60-fold quotients : {2,4}*16
   80-fold quotients : {3,2}*12
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,16}*1920a, {30,32}*1920
Permutation Representation (GAP) :
s0 := (  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 17, 20)
( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)
( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)
( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)( 67, 75)
( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)
( 84, 88)( 85, 87)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)( 99,103)
(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)(115,117)
(122,125)(123,124)(126,131)(127,135)(128,134)(129,133)(130,132)(137,140)
(138,139)(141,146)(142,150)(143,149)(144,148)(145,147)(152,155)(153,154)
(156,161)(157,165)(158,164)(159,163)(160,162)(167,170)(168,169)(171,176)
(172,180)(173,179)(174,178)(175,177)(182,185)(183,184)(186,191)(187,195)
(188,194)(189,193)(190,192)(197,200)(198,199)(201,206)(202,210)(203,209)
(204,208)(205,207)(212,215)(213,214)(216,221)(217,225)(218,224)(219,223)
(220,222)(227,230)(228,229)(231,236)(232,240)(233,239)(234,238)(235,237);;
s1 := (  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, 52)( 32, 51)
( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)( 40, 48)
( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 97)( 62, 96)( 63,100)
( 64, 99)( 65, 98)( 66, 92)( 67, 91)( 68, 95)( 69, 94)( 70, 93)( 71,102)
( 72,101)( 73,105)( 74,104)( 75,103)( 76,112)( 77,111)( 78,115)( 79,114)
( 80,113)( 81,107)( 82,106)( 83,110)( 84,109)( 85,108)( 86,117)( 87,116)
( 88,120)( 89,119)( 90,118)(121,187)(122,186)(123,190)(124,189)(125,188)
(126,182)(127,181)(128,185)(129,184)(130,183)(131,192)(132,191)(133,195)
(134,194)(135,193)(136,202)(137,201)(138,205)(139,204)(140,203)(141,197)
(142,196)(143,200)(144,199)(145,198)(146,207)(147,206)(148,210)(149,209)
(150,208)(151,232)(152,231)(153,235)(154,234)(155,233)(156,227)(157,226)
(158,230)(159,229)(160,228)(161,237)(162,236)(163,240)(164,239)(165,238)
(166,217)(167,216)(168,220)(169,219)(170,218)(171,212)(172,211)(173,215)
(174,214)(175,213)(176,222)(177,221)(178,225)(179,224)(180,223);;
s2 := (  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)( 31,166)( 32,167)
( 33,168)( 34,169)( 35,170)( 36,171)( 37,172)( 38,173)( 39,174)( 40,175)
( 41,176)( 42,177)( 43,178)( 44,179)( 45,180)( 46,151)( 47,152)( 48,153)
( 49,154)( 50,155)( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)
( 57,162)( 58,163)( 59,164)( 60,165)( 61,211)( 62,212)( 63,213)( 64,214)
( 65,215)( 66,216)( 67,217)( 68,218)( 69,219)( 70,220)( 71,221)( 72,222)
( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)( 80,230)
( 81,231)( 82,232)( 83,233)( 84,234)( 85,235)( 86,236)( 87,237)( 88,238)
( 89,239)( 90,240)( 91,181)( 92,182)( 93,183)( 94,184)( 95,185)( 96,186)
( 97,187)( 98,188)( 99,189)(100,190)(101,191)(102,192)(103,193)(104,194)
(105,195)(106,196)(107,197)(108,198)(109,199)(110,200)(111,201)(112,202)
(113,203)(114,204)(115,205)(116,206)(117,207)(118,208)(119,209)(120,210);;
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, s0*s1*s2*s1*s0*s1*s2*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, 
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)!(  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)
( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)
( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)
( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)
( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)
( 83, 89)( 84, 88)( 85, 87)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)
( 99,103)(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)
(115,117)(122,125)(123,124)(126,131)(127,135)(128,134)(129,133)(130,132)
(137,140)(138,139)(141,146)(142,150)(143,149)(144,148)(145,147)(152,155)
(153,154)(156,161)(157,165)(158,164)(159,163)(160,162)(167,170)(168,169)
(171,176)(172,180)(173,179)(174,178)(175,177)(182,185)(183,184)(186,191)
(187,195)(188,194)(189,193)(190,192)(197,200)(198,199)(201,206)(202,210)
(203,209)(204,208)(205,207)(212,215)(213,214)(216,221)(217,225)(218,224)
(219,223)(220,222)(227,230)(228,229)(231,236)(232,240)(233,239)(234,238)
(235,237);
s1 := 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, 52)
( 32, 51)( 33, 55)( 34, 54)( 35, 53)( 36, 47)( 37, 46)( 38, 50)( 39, 49)
( 40, 48)( 41, 57)( 42, 56)( 43, 60)( 44, 59)( 45, 58)( 61, 97)( 62, 96)
( 63,100)( 64, 99)( 65, 98)( 66, 92)( 67, 91)( 68, 95)( 69, 94)( 70, 93)
( 71,102)( 72,101)( 73,105)( 74,104)( 75,103)( 76,112)( 77,111)( 78,115)
( 79,114)( 80,113)( 81,107)( 82,106)( 83,110)( 84,109)( 85,108)( 86,117)
( 87,116)( 88,120)( 89,119)( 90,118)(121,187)(122,186)(123,190)(124,189)
(125,188)(126,182)(127,181)(128,185)(129,184)(130,183)(131,192)(132,191)
(133,195)(134,194)(135,193)(136,202)(137,201)(138,205)(139,204)(140,203)
(141,197)(142,196)(143,200)(144,199)(145,198)(146,207)(147,206)(148,210)
(149,209)(150,208)(151,232)(152,231)(153,235)(154,234)(155,233)(156,227)
(157,226)(158,230)(159,229)(160,228)(161,237)(162,236)(163,240)(164,239)
(165,238)(166,217)(167,216)(168,220)(169,219)(170,218)(171,212)(172,211)
(173,215)(174,214)(175,213)(176,222)(177,221)(178,225)(179,224)(180,223);
s2 := 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)( 31,166)
( 32,167)( 33,168)( 34,169)( 35,170)( 36,171)( 37,172)( 38,173)( 39,174)
( 40,175)( 41,176)( 42,177)( 43,178)( 44,179)( 45,180)( 46,151)( 47,152)
( 48,153)( 49,154)( 50,155)( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)
( 56,161)( 57,162)( 58,163)( 59,164)( 60,165)( 61,211)( 62,212)( 63,213)
( 64,214)( 65,215)( 66,216)( 67,217)( 68,218)( 69,219)( 70,220)( 71,221)
( 72,222)( 73,223)( 74,224)( 75,225)( 76,226)( 77,227)( 78,228)( 79,229)
( 80,230)( 81,231)( 82,232)( 83,233)( 84,234)( 85,235)( 86,236)( 87,237)
( 88,238)( 89,239)( 90,240)( 91,181)( 92,182)( 93,183)( 94,184)( 95,185)
( 96,186)( 97,187)( 98,188)( 99,189)(100,190)(101,191)(102,192)(103,193)
(104,194)(105,195)(106,196)(107,197)(108,198)(109,199)(110,200)(111,201)
(112,202)(113,203)(114,204)(115,205)(116,206)(117,207)(118,208)(119,209)
(120,210);
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, s0*s1*s2*s1*s0*s1*s2*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, 
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