Polytope of Type {16,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,30}*960
Also Known As : {16,30|2}. if this polytope has another name.
Group : SmallGroup(960,5206)
Rank : 3
Schlafli Type : {16,30}
Number of vertices, edges, etc : 16, 240, 30
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 :
   {16,30,2} of size 1920
Vertex Figure Of :
   {2,16,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,30}*480
   3-fold quotients : {16,10}*320
   4-fold quotients : {4,30}*240a
   5-fold quotients : {16,6}*192
   6-fold quotients : {8,10}*160
   8-fold quotients : {2,30}*120
   10-fold quotients : {8,6}*96
   12-fold quotients : {4,10}*80
   15-fold quotients : {16,2}*64
   16-fold quotients : {2,15}*60
   20-fold quotients : {4,6}*48a
   24-fold quotients : {2,10}*40
   30-fold quotients : {8,2}*32
   40-fold quotients : {2,6}*24
   48-fold quotients : {2,5}*20
   60-fold quotients : {4,2}*16
   80-fold quotients : {2,3}*12
   120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {16,60}*1920a, {32,30}*1920
Permutation Representation (GAP) :

s0 := ( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 53)
( 39, 54)( 40, 55)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)( 61, 91)
( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68, 98)( 69, 99)
( 70,100)( 71,101)( 72,102)( 73,103)( 74,104)( 75,105)( 76,106)( 77,107)
( 78,108)( 79,109)( 80,110)( 81,111)( 82,112)( 83,113)( 84,114)( 85,115)
( 86,116)( 87,117)( 88,118)( 89,119)( 90,120)(121,181)(122,182)(123,183)
(124,184)(125,185)(126,186)(127,187)(128,188)(129,189)(130,190)(131,191)
(132,192)(133,193)(134,194)(135,195)(136,196)(137,197)(138,198)(139,199)
(140,200)(141,201)(142,202)(143,203)(144,204)(145,205)(146,206)(147,207)
(148,208)(149,209)(150,210)(151,226)(152,227)(153,228)(154,229)(155,230)
(156,231)(157,232)(158,233)(159,234)(160,235)(161,236)(162,237)(163,238)
(164,239)(165,240)(166,211)(167,212)(168,213)(169,214)(170,215)(171,216)
(172,217)(173,218)(174,219)(175,220)(176,221)(177,222)(178,223)(179,224)
(180,225);;
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)( 31,166)( 32,170)
( 33,169)( 34,168)( 35,167)( 36,176)( 37,180)( 38,179)( 39,178)( 40,177)
( 41,171)( 42,175)( 43,174)( 44,173)( 45,172)( 46,151)( 47,155)( 48,154)
( 49,153)( 50,152)( 51,161)( 52,165)( 53,164)( 54,163)( 55,162)( 56,156)
( 57,160)( 58,159)( 59,158)( 60,157)( 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, 67)( 62, 66)( 63, 70)( 64, 69)
( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)( 80, 83)
( 86, 87)( 88, 90)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)(101,102)
(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)(118,120)
(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)(181,187)(182,186)(183,190)(184,189)
(185,188)(191,192)(193,195)(196,202)(197,201)(198,205)(199,204)(200,203)
(206,207)(208,210)(211,217)(212,216)(213,220)(214,219)(215,218)(221,222)
(223,225)(226,232)(227,231)(228,235)(229,234)(230,233)(236,237)(238,240);;
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, 
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, 
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)!( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)
( 38, 53)( 39, 54)( 40, 55)( 41, 56)( 42, 57)( 43, 58)( 44, 59)( 45, 60)
( 61, 91)( 62, 92)( 63, 93)( 64, 94)( 65, 95)( 66, 96)( 67, 97)( 68, 98)
( 69, 99)( 70,100)( 71,101)( 72,102)( 73,103)( 74,104)( 75,105)( 76,106)
( 77,107)( 78,108)( 79,109)( 80,110)( 81,111)( 82,112)( 83,113)( 84,114)
( 85,115)( 86,116)( 87,117)( 88,118)( 89,119)( 90,120)(121,181)(122,182)
(123,183)(124,184)(125,185)(126,186)(127,187)(128,188)(129,189)(130,190)
(131,191)(132,192)(133,193)(134,194)(135,195)(136,196)(137,197)(138,198)
(139,199)(140,200)(141,201)(142,202)(143,203)(144,204)(145,205)(146,206)
(147,207)(148,208)(149,209)(150,210)(151,226)(152,227)(153,228)(154,229)
(155,230)(156,231)(157,232)(158,233)(159,234)(160,235)(161,236)(162,237)
(163,238)(164,239)(165,240)(166,211)(167,212)(168,213)(169,214)(170,215)
(171,216)(172,217)(173,218)(174,219)(175,220)(176,221)(177,222)(178,223)
(179,224)(180,225);
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)( 31,166)
( 32,170)( 33,169)( 34,168)( 35,167)( 36,176)( 37,180)( 38,179)( 39,178)
( 40,177)( 41,171)( 42,175)( 43,174)( 44,173)( 45,172)( 46,151)( 47,155)
( 48,154)( 49,153)( 50,152)( 51,161)( 52,165)( 53,164)( 54,163)( 55,162)
( 56,156)( 57,160)( 58,159)( 59,158)( 60,157)( 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, 67)( 62, 66)( 63, 70)
( 64, 69)( 65, 68)( 71, 72)( 73, 75)( 76, 82)( 77, 81)( 78, 85)( 79, 84)
( 80, 83)( 86, 87)( 88, 90)( 91, 97)( 92, 96)( 93,100)( 94, 99)( 95, 98)
(101,102)(103,105)(106,112)(107,111)(108,115)(109,114)(110,113)(116,117)
(118,120)(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)(181,187)(182,186)(183,190)
(184,189)(185,188)(191,192)(193,195)(196,202)(197,201)(198,205)(199,204)
(200,203)(206,207)(208,210)(211,217)(212,216)(213,220)(214,219)(215,218)
(221,222)(223,225)(226,232)(227,231)(228,235)(229,234)(230,233)(236,237)
(238,240);
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, 
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, 
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