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