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