Polytope of Type {2,15,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,15,8}*960
if this polytope has a name.
Group : SmallGroup(960,11101)
Rank : 4
Schlafli Type : {2,15,8}
Number of vertices, edges, etc : 2, 30, 120, 16
Order of s0s1s2s3 : 60
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,15,8,2} of size 1920
Vertex Figure Of :
{2,2,15,8} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,15,4}*480
4-fold quotients : {2,15,4}*240
5-fold quotients : {2,3,8}*192
8-fold quotients : {2,15,2}*120
10-fold quotients : {2,3,4}*96
20-fold quotients : {2,3,4}*48
24-fold quotients : {2,5,2}*40
40-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,30,8}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 7)( 6, 8)( 9, 10)( 11, 35)( 12, 36)( 13, 39)( 14, 40)( 15, 37)
( 16, 38)( 17, 42)( 18, 41)( 19, 27)( 20, 28)( 21, 31)( 22, 32)( 23, 29)
( 24, 30)( 25, 34)( 26, 33)( 43, 83)( 44, 84)( 45, 87)( 46, 88)( 47, 85)
( 48, 86)( 49, 90)( 50, 89)( 51,115)( 52,116)( 53,119)( 54,120)( 55,117)
( 56,118)( 57,122)( 58,121)( 59,107)( 60,108)( 61,111)( 62,112)( 63,109)
( 64,110)( 65,114)( 66,113)( 67, 99)( 68,100)( 69,103)( 70,104)( 71,101)
( 72,102)( 73,106)( 74,105)( 75, 91)( 76, 92)( 77, 95)( 78, 96)( 79, 93)
( 80, 94)( 81, 98)( 82, 97)(123,124)(125,128)(126,127)(131,156)(132,155)
(133,160)(134,159)(135,158)(136,157)(137,161)(138,162)(139,148)(140,147)
(141,152)(142,151)(143,150)(144,149)(145,153)(146,154)(163,204)(164,203)
(165,208)(166,207)(167,206)(168,205)(169,209)(170,210)(171,236)(172,235)
(173,240)(174,239)(175,238)(176,237)(177,241)(178,242)(179,228)(180,227)
(181,232)(182,231)(183,230)(184,229)(185,233)(186,234)(187,220)(188,219)
(189,224)(190,223)(191,222)(192,221)(193,225)(194,226)(195,212)(196,211)
(197,216)(198,215)(199,214)(200,213)(201,217)(202,218);;
s2 := ( 3, 51)( 4, 52)( 5, 54)( 6, 53)( 7, 57)( 8, 58)( 9, 55)( 10, 56)
( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 49)( 16, 50)( 17, 47)( 18, 48)
( 19, 75)( 20, 76)( 21, 78)( 22, 77)( 23, 81)( 24, 82)( 25, 79)( 26, 80)
( 27, 67)( 28, 68)( 29, 70)( 30, 69)( 31, 73)( 32, 74)( 33, 71)( 34, 72)
( 35, 59)( 36, 60)( 37, 62)( 38, 61)( 39, 65)( 40, 66)( 41, 63)( 42, 64)
( 83, 91)( 84, 92)( 85, 94)( 86, 93)( 87, 97)( 88, 98)( 89, 95)( 90, 96)
( 99,115)(100,116)(101,118)(102,117)(103,121)(104,122)(105,119)(106,120)
(109,110)(111,113)(112,114)(123,172)(124,171)(125,173)(126,174)(127,178)
(128,177)(129,176)(130,175)(131,164)(132,163)(133,165)(134,166)(135,170)
(136,169)(137,168)(138,167)(139,196)(140,195)(141,197)(142,198)(143,202)
(144,201)(145,200)(146,199)(147,188)(148,187)(149,189)(150,190)(151,194)
(152,193)(153,192)(154,191)(155,180)(156,179)(157,181)(158,182)(159,186)
(160,185)(161,184)(162,183)(203,212)(204,211)(205,213)(206,214)(207,218)
(208,217)(209,216)(210,215)(219,236)(220,235)(221,237)(222,238)(223,242)
(224,241)(225,240)(226,239)(227,228)(231,234)(232,233);;
s3 := ( 3,129)( 4,130)( 5,127)( 6,128)( 7,126)( 8,125)( 9,124)( 10,123)
( 11,137)( 12,138)( 13,135)( 14,136)( 15,134)( 16,133)( 17,132)( 18,131)
( 19,145)( 20,146)( 21,143)( 22,144)( 23,142)( 24,141)( 25,140)( 26,139)
( 27,153)( 28,154)( 29,151)( 30,152)( 31,150)( 32,149)( 33,148)( 34,147)
( 35,161)( 36,162)( 37,159)( 38,160)( 39,158)( 40,157)( 41,156)( 42,155)
( 43,169)( 44,170)( 45,167)( 46,168)( 47,166)( 48,165)( 49,164)( 50,163)
( 51,177)( 52,178)( 53,175)( 54,176)( 55,174)( 56,173)( 57,172)( 58,171)
( 59,185)( 60,186)( 61,183)( 62,184)( 63,182)( 64,181)( 65,180)( 66,179)
( 67,193)( 68,194)( 69,191)( 70,192)( 71,190)( 72,189)( 73,188)( 74,187)
( 75,201)( 76,202)( 77,199)( 78,200)( 79,198)( 80,197)( 81,196)( 82,195)
( 83,209)( 84,210)( 85,207)( 86,208)( 87,206)( 88,205)( 89,204)( 90,203)
( 91,217)( 92,218)( 93,215)( 94,216)( 95,214)( 96,213)( 97,212)( 98,211)
( 99,225)(100,226)(101,223)(102,224)(103,222)(104,221)(105,220)(106,219)
(107,233)(108,234)(109,231)(110,232)(111,230)(112,229)(113,228)(114,227)
(115,241)(116,242)(117,239)(118,240)(119,238)(120,237)(121,236)(122,235);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*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(242)!(1,2);
s1 := Sym(242)!( 5, 7)( 6, 8)( 9, 10)( 11, 35)( 12, 36)( 13, 39)( 14, 40)
( 15, 37)( 16, 38)( 17, 42)( 18, 41)( 19, 27)( 20, 28)( 21, 31)( 22, 32)
( 23, 29)( 24, 30)( 25, 34)( 26, 33)( 43, 83)( 44, 84)( 45, 87)( 46, 88)
( 47, 85)( 48, 86)( 49, 90)( 50, 89)( 51,115)( 52,116)( 53,119)( 54,120)
( 55,117)( 56,118)( 57,122)( 58,121)( 59,107)( 60,108)( 61,111)( 62,112)
( 63,109)( 64,110)( 65,114)( 66,113)( 67, 99)( 68,100)( 69,103)( 70,104)
( 71,101)( 72,102)( 73,106)( 74,105)( 75, 91)( 76, 92)( 77, 95)( 78, 96)
( 79, 93)( 80, 94)( 81, 98)( 82, 97)(123,124)(125,128)(126,127)(131,156)
(132,155)(133,160)(134,159)(135,158)(136,157)(137,161)(138,162)(139,148)
(140,147)(141,152)(142,151)(143,150)(144,149)(145,153)(146,154)(163,204)
(164,203)(165,208)(166,207)(167,206)(168,205)(169,209)(170,210)(171,236)
(172,235)(173,240)(174,239)(175,238)(176,237)(177,241)(178,242)(179,228)
(180,227)(181,232)(182,231)(183,230)(184,229)(185,233)(186,234)(187,220)
(188,219)(189,224)(190,223)(191,222)(192,221)(193,225)(194,226)(195,212)
(196,211)(197,216)(198,215)(199,214)(200,213)(201,217)(202,218);
s2 := Sym(242)!( 3, 51)( 4, 52)( 5, 54)( 6, 53)( 7, 57)( 8, 58)( 9, 55)
( 10, 56)( 11, 43)( 12, 44)( 13, 46)( 14, 45)( 15, 49)( 16, 50)( 17, 47)
( 18, 48)( 19, 75)( 20, 76)( 21, 78)( 22, 77)( 23, 81)( 24, 82)( 25, 79)
( 26, 80)( 27, 67)( 28, 68)( 29, 70)( 30, 69)( 31, 73)( 32, 74)( 33, 71)
( 34, 72)( 35, 59)( 36, 60)( 37, 62)( 38, 61)( 39, 65)( 40, 66)( 41, 63)
( 42, 64)( 83, 91)( 84, 92)( 85, 94)( 86, 93)( 87, 97)( 88, 98)( 89, 95)
( 90, 96)( 99,115)(100,116)(101,118)(102,117)(103,121)(104,122)(105,119)
(106,120)(109,110)(111,113)(112,114)(123,172)(124,171)(125,173)(126,174)
(127,178)(128,177)(129,176)(130,175)(131,164)(132,163)(133,165)(134,166)
(135,170)(136,169)(137,168)(138,167)(139,196)(140,195)(141,197)(142,198)
(143,202)(144,201)(145,200)(146,199)(147,188)(148,187)(149,189)(150,190)
(151,194)(152,193)(153,192)(154,191)(155,180)(156,179)(157,181)(158,182)
(159,186)(160,185)(161,184)(162,183)(203,212)(204,211)(205,213)(206,214)
(207,218)(208,217)(209,216)(210,215)(219,236)(220,235)(221,237)(222,238)
(223,242)(224,241)(225,240)(226,239)(227,228)(231,234)(232,233);
s3 := Sym(242)!( 3,129)( 4,130)( 5,127)( 6,128)( 7,126)( 8,125)( 9,124)
( 10,123)( 11,137)( 12,138)( 13,135)( 14,136)( 15,134)( 16,133)( 17,132)
( 18,131)( 19,145)( 20,146)( 21,143)( 22,144)( 23,142)( 24,141)( 25,140)
( 26,139)( 27,153)( 28,154)( 29,151)( 30,152)( 31,150)( 32,149)( 33,148)
( 34,147)( 35,161)( 36,162)( 37,159)( 38,160)( 39,158)( 40,157)( 41,156)
( 42,155)( 43,169)( 44,170)( 45,167)( 46,168)( 47,166)( 48,165)( 49,164)
( 50,163)( 51,177)( 52,178)( 53,175)( 54,176)( 55,174)( 56,173)( 57,172)
( 58,171)( 59,185)( 60,186)( 61,183)( 62,184)( 63,182)( 64,181)( 65,180)
( 66,179)( 67,193)( 68,194)( 69,191)( 70,192)( 71,190)( 72,189)( 73,188)
( 74,187)( 75,201)( 76,202)( 77,199)( 78,200)( 79,198)( 80,197)( 81,196)
( 82,195)( 83,209)( 84,210)( 85,207)( 86,208)( 87,206)( 88,205)( 89,204)
( 90,203)( 91,217)( 92,218)( 93,215)( 94,216)( 95,214)( 96,213)( 97,212)
( 98,211)( 99,225)(100,226)(101,223)(102,224)(103,222)(104,221)(105,220)
(106,219)(107,233)(108,234)(109,231)(110,232)(111,230)(112,229)(113,228)
(114,227)(115,241)(116,242)(117,239)(118,240)(119,238)(120,237)(121,236)
(122,235);
poly := sub<Sym(242)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*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 >;
to this polytope