Polytope of Type {12,30}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,30}*960b
if this polytope has a name.
Group : SmallGroup(960,10994)
Rank : 3
Schlafli Type : {12,30}
Number of vertices, edges, etc : 16, 240, 40
Order of s0s1s2 : 20
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{12,30,2} of size 1920
Vertex Figure Of :
{2,12,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,30}*480
4-fold quotients : {6,15}*240
5-fold quotients : {12,6}*192a
10-fold quotients : {6,6}*96
12-fold quotients : {4,10}*80
20-fold quotients : {3,6}*48, {6,3}*48
24-fold quotients : {2,10}*40
40-fold quotients : {3,3}*24
48-fold quotients : {2,5}*20
60-fold quotients : {4,2}*16
120-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,60}*1920c, {24,30}*1920a, {12,30}*1920, {12,60}*1920d, {24,30}*1920b
Permutation Representation (GAP) :
s0 := ( 2, 3)( 6, 7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)( 23, 42)
( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)( 31, 50)
( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)( 39, 58)
( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)( 90,111)
( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)( 98,119)
( 99,118)(100,120)(121,181)(122,183)(123,182)(124,184)(125,185)(126,187)
(127,186)(128,188)(129,189)(130,191)(131,190)(132,192)(133,193)(134,195)
(135,194)(136,196)(137,197)(138,199)(139,198)(140,200)(141,221)(142,223)
(143,222)(144,224)(145,225)(146,227)(147,226)(148,228)(149,229)(150,231)
(151,230)(152,232)(153,233)(154,235)(155,234)(156,236)(157,237)(158,239)
(159,238)(160,240)(161,201)(162,203)(163,202)(164,204)(165,205)(166,207)
(167,206)(168,208)(169,209)(170,211)(171,210)(172,212)(173,213)(174,215)
(175,214)(176,216)(177,217)(178,219)(179,218)(180,220);;
s1 := ( 1,141)( 2,142)( 3,144)( 4,143)( 5,157)( 6,158)( 7,160)( 8,159)
( 9,153)( 10,154)( 11,156)( 12,155)( 13,149)( 14,150)( 15,152)( 16,151)
( 17,145)( 18,146)( 19,148)( 20,147)( 21,121)( 22,122)( 23,124)( 24,123)
( 25,137)( 26,138)( 27,140)( 28,139)( 29,133)( 30,134)( 31,136)( 32,135)
( 33,129)( 34,130)( 35,132)( 36,131)( 37,125)( 38,126)( 39,128)( 40,127)
( 41,161)( 42,162)( 43,164)( 44,163)( 45,177)( 46,178)( 47,180)( 48,179)
( 49,173)( 50,174)( 51,176)( 52,175)( 53,169)( 54,170)( 55,172)( 56,171)
( 57,165)( 58,166)( 59,168)( 60,167)( 61,201)( 62,202)( 63,204)( 64,203)
( 65,217)( 66,218)( 67,220)( 68,219)( 69,213)( 70,214)( 71,216)( 72,215)
( 73,209)( 74,210)( 75,212)( 76,211)( 77,205)( 78,206)( 79,208)( 80,207)
( 81,181)( 82,182)( 83,184)( 84,183)( 85,197)( 86,198)( 87,200)( 88,199)
( 89,193)( 90,194)( 91,196)( 92,195)( 93,189)( 94,190)( 95,192)( 96,191)
( 97,185)( 98,186)( 99,188)(100,187)(101,221)(102,222)(103,224)(104,223)
(105,237)(106,238)(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)
(113,229)(114,230)(115,232)(116,231)(117,225)(118,226)(119,228)(120,227);;
s2 := ( 1, 8)( 2, 6)( 3, 7)( 4, 5)( 9, 20)( 10, 18)( 11, 19)( 12, 17)
( 13, 16)( 21, 48)( 22, 46)( 23, 47)( 24, 45)( 25, 44)( 26, 42)( 27, 43)
( 28, 41)( 29, 60)( 30, 58)( 31, 59)( 32, 57)( 33, 56)( 34, 54)( 35, 55)
( 36, 53)( 37, 52)( 38, 50)( 39, 51)( 40, 49)( 61, 68)( 62, 66)( 63, 67)
( 64, 65)( 69, 80)( 70, 78)( 71, 79)( 72, 77)( 73, 76)( 81,108)( 82,106)
( 83,107)( 84,105)( 85,104)( 86,102)( 87,103)( 88,101)( 89,120)( 90,118)
( 91,119)( 92,117)( 93,116)( 94,114)( 95,115)( 96,113)( 97,112)( 98,110)
( 99,111)(100,109)(121,128)(122,126)(123,127)(124,125)(129,140)(130,138)
(131,139)(132,137)(133,136)(141,168)(142,166)(143,167)(144,165)(145,164)
(146,162)(147,163)(148,161)(149,180)(150,178)(151,179)(152,177)(153,176)
(154,174)(155,175)(156,173)(157,172)(158,170)(159,171)(160,169)(181,188)
(182,186)(183,187)(184,185)(189,200)(190,198)(191,199)(192,197)(193,196)
(201,228)(202,226)(203,227)(204,225)(205,224)(206,222)(207,223)(208,221)
(209,240)(210,238)(211,239)(212,237)(213,236)(214,234)(215,235)(216,233)
(217,232)(218,230)(219,231)(220,229);;
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*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(240)!( 2, 3)( 6, 7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)
( 23, 42)( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)
( 31, 50)( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)
( 39, 58)( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)
( 82,103)( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)
( 90,111)( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)
( 98,119)( 99,118)(100,120)(121,181)(122,183)(123,182)(124,184)(125,185)
(126,187)(127,186)(128,188)(129,189)(130,191)(131,190)(132,192)(133,193)
(134,195)(135,194)(136,196)(137,197)(138,199)(139,198)(140,200)(141,221)
(142,223)(143,222)(144,224)(145,225)(146,227)(147,226)(148,228)(149,229)
(150,231)(151,230)(152,232)(153,233)(154,235)(155,234)(156,236)(157,237)
(158,239)(159,238)(160,240)(161,201)(162,203)(163,202)(164,204)(165,205)
(166,207)(167,206)(168,208)(169,209)(170,211)(171,210)(172,212)(173,213)
(174,215)(175,214)(176,216)(177,217)(178,219)(179,218)(180,220);
s1 := Sym(240)!( 1,141)( 2,142)( 3,144)( 4,143)( 5,157)( 6,158)( 7,160)
( 8,159)( 9,153)( 10,154)( 11,156)( 12,155)( 13,149)( 14,150)( 15,152)
( 16,151)( 17,145)( 18,146)( 19,148)( 20,147)( 21,121)( 22,122)( 23,124)
( 24,123)( 25,137)( 26,138)( 27,140)( 28,139)( 29,133)( 30,134)( 31,136)
( 32,135)( 33,129)( 34,130)( 35,132)( 36,131)( 37,125)( 38,126)( 39,128)
( 40,127)( 41,161)( 42,162)( 43,164)( 44,163)( 45,177)( 46,178)( 47,180)
( 48,179)( 49,173)( 50,174)( 51,176)( 52,175)( 53,169)( 54,170)( 55,172)
( 56,171)( 57,165)( 58,166)( 59,168)( 60,167)( 61,201)( 62,202)( 63,204)
( 64,203)( 65,217)( 66,218)( 67,220)( 68,219)( 69,213)( 70,214)( 71,216)
( 72,215)( 73,209)( 74,210)( 75,212)( 76,211)( 77,205)( 78,206)( 79,208)
( 80,207)( 81,181)( 82,182)( 83,184)( 84,183)( 85,197)( 86,198)( 87,200)
( 88,199)( 89,193)( 90,194)( 91,196)( 92,195)( 93,189)( 94,190)( 95,192)
( 96,191)( 97,185)( 98,186)( 99,188)(100,187)(101,221)(102,222)(103,224)
(104,223)(105,237)(106,238)(107,240)(108,239)(109,233)(110,234)(111,236)
(112,235)(113,229)(114,230)(115,232)(116,231)(117,225)(118,226)(119,228)
(120,227);
s2 := Sym(240)!( 1, 8)( 2, 6)( 3, 7)( 4, 5)( 9, 20)( 10, 18)( 11, 19)
( 12, 17)( 13, 16)( 21, 48)( 22, 46)( 23, 47)( 24, 45)( 25, 44)( 26, 42)
( 27, 43)( 28, 41)( 29, 60)( 30, 58)( 31, 59)( 32, 57)( 33, 56)( 34, 54)
( 35, 55)( 36, 53)( 37, 52)( 38, 50)( 39, 51)( 40, 49)( 61, 68)( 62, 66)
( 63, 67)( 64, 65)( 69, 80)( 70, 78)( 71, 79)( 72, 77)( 73, 76)( 81,108)
( 82,106)( 83,107)( 84,105)( 85,104)( 86,102)( 87,103)( 88,101)( 89,120)
( 90,118)( 91,119)( 92,117)( 93,116)( 94,114)( 95,115)( 96,113)( 97,112)
( 98,110)( 99,111)(100,109)(121,128)(122,126)(123,127)(124,125)(129,140)
(130,138)(131,139)(132,137)(133,136)(141,168)(142,166)(143,167)(144,165)
(145,164)(146,162)(147,163)(148,161)(149,180)(150,178)(151,179)(152,177)
(153,176)(154,174)(155,175)(156,173)(157,172)(158,170)(159,171)(160,169)
(181,188)(182,186)(183,187)(184,185)(189,200)(190,198)(191,199)(192,197)
(193,196)(201,228)(202,226)(203,227)(204,225)(205,224)(206,222)(207,223)
(208,221)(209,240)(210,238)(211,239)(212,237)(213,236)(214,234)(215,235)
(216,233)(217,232)(218,230)(219,231)(220,229);
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*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*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 >;
References : None.
to this polytope