Polytope of Type {2,4,4,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,4,15}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240291)
Rank : 5
Schlafli Type : {2,4,4,15}
Number of vertices, edges, etc : 2, 4, 16, 60, 30
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,2,4,15}*960
4-fold quotients : {2,4,2,15}*480, {2,2,4,15}*480
5-fold quotients : {2,4,4,3}*384b
8-fold quotients : {2,2,2,15}*240
10-fold quotients : {2,2,4,3}*192
12-fold quotients : {2,4,2,5}*160
20-fold quotients : {2,4,2,3}*96, {2,2,4,3}*96
24-fold quotients : {2,2,2,5}*80
40-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (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)(151,211)(152,212)(153,213)(154,214)
(155,215)(156,216)(157,217)(158,218)(159,219)(160,220)(161,221)(162,222)
(163,223)(164,224)(165,225)(166,226)(167,227)(168,228)(169,229)(170,230)
(171,231)(172,232)(173,233)(174,234)(175,235)(176,236)(177,237)(178,238)
(179,239)(180,240)(181,241)(182,242);;
s2 := ( 3,125)( 4,126)( 5,123)( 6,124)( 7,129)( 8,130)( 9,127)( 10,128)
( 11,133)( 12,134)( 13,131)( 14,132)( 15,137)( 16,138)( 17,135)( 18,136)
( 19,141)( 20,142)( 21,139)( 22,140)( 23,145)( 24,146)( 25,143)( 26,144)
( 27,149)( 28,150)( 29,147)( 30,148)( 31,153)( 32,154)( 33,151)( 34,152)
( 35,157)( 36,158)( 37,155)( 38,156)( 39,161)( 40,162)( 41,159)( 42,160)
( 43,165)( 44,166)( 45,163)( 46,164)( 47,169)( 48,170)( 49,167)( 50,168)
( 51,173)( 52,174)( 53,171)( 54,172)( 55,177)( 56,178)( 57,175)( 58,176)
( 59,181)( 60,182)( 61,179)( 62,180)( 63,185)( 64,186)( 65,183)( 66,184)
( 67,189)( 68,190)( 69,187)( 70,188)( 71,193)( 72,194)( 73,191)( 74,192)
( 75,197)( 76,198)( 77,195)( 78,196)( 79,201)( 80,202)( 81,199)( 82,200)
( 83,205)( 84,206)( 85,203)( 86,204)( 87,209)( 88,210)( 89,207)( 90,208)
( 91,213)( 92,214)( 93,211)( 94,212)( 95,217)( 96,218)( 97,215)( 98,216)
( 99,221)(100,222)(101,219)(102,220)(103,225)(104,226)(105,223)(106,224)
(107,229)(108,230)(109,227)(110,228)(111,233)(112,234)(113,231)(114,232)
(115,237)(116,238)(117,235)(118,236)(119,241)(120,242)(121,239)(122,240);;
s3 := ( 4, 5)( 7, 19)( 8, 21)( 9, 20)( 10, 22)( 11, 15)( 12, 17)( 13, 16)
( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)( 29, 60)
( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)( 37, 52)
( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)( 68, 81)
( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)( 84,105)
( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)( 92,117)
( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)(100,109)
(101,108)(102,110)(124,125)(127,139)(128,141)(129,140)(130,142)(131,135)
(132,137)(133,136)(134,138)(143,163)(144,165)(145,164)(146,166)(147,179)
(148,181)(149,180)(150,182)(151,175)(152,177)(153,176)(154,178)(155,171)
(156,173)(157,172)(158,174)(159,167)(160,169)(161,168)(162,170)(184,185)
(187,199)(188,201)(189,200)(190,202)(191,195)(192,197)(193,196)(194,198)
(203,223)(204,225)(205,224)(206,226)(207,239)(208,241)(209,240)(210,242)
(211,235)(212,237)(213,236)(214,238)(215,231)(216,233)(217,232)(218,234)
(219,227)(220,229)(221,228)(222,230);;
s4 := ( 3, 47)( 4, 50)( 5, 49)( 6, 48)( 7, 43)( 8, 46)( 9, 45)( 10, 44)
( 11, 59)( 12, 62)( 13, 61)( 14, 60)( 15, 55)( 16, 58)( 17, 57)( 18, 56)
( 19, 51)( 20, 54)( 21, 53)( 22, 52)( 23, 27)( 24, 30)( 25, 29)( 26, 28)
( 31, 39)( 32, 42)( 33, 41)( 34, 40)( 36, 38)( 63,107)( 64,110)( 65,109)
( 66,108)( 67,103)( 68,106)( 69,105)( 70,104)( 71,119)( 72,122)( 73,121)
( 74,120)( 75,115)( 76,118)( 77,117)( 78,116)( 79,111)( 80,114)( 81,113)
( 82,112)( 83, 87)( 84, 90)( 85, 89)( 86, 88)( 91, 99)( 92,102)( 93,101)
( 94,100)( 96, 98)(123,167)(124,170)(125,169)(126,168)(127,163)(128,166)
(129,165)(130,164)(131,179)(132,182)(133,181)(134,180)(135,175)(136,178)
(137,177)(138,176)(139,171)(140,174)(141,173)(142,172)(143,147)(144,150)
(145,149)(146,148)(151,159)(152,162)(153,161)(154,160)(156,158)(183,227)
(184,230)(185,229)(186,228)(187,223)(188,226)(189,225)(190,224)(191,239)
(192,242)(193,241)(194,240)(195,235)(196,238)(197,237)(198,236)(199,231)
(200,234)(201,233)(202,232)(203,207)(204,210)(205,209)(206,208)(211,219)
(212,222)(213,221)(214,220)(216,218);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!(1,2);
s1 := Sym(242)!(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)(151,211)(152,212)(153,213)
(154,214)(155,215)(156,216)(157,217)(158,218)(159,219)(160,220)(161,221)
(162,222)(163,223)(164,224)(165,225)(166,226)(167,227)(168,228)(169,229)
(170,230)(171,231)(172,232)(173,233)(174,234)(175,235)(176,236)(177,237)
(178,238)(179,239)(180,240)(181,241)(182,242);
s2 := Sym(242)!( 3,125)( 4,126)( 5,123)( 6,124)( 7,129)( 8,130)( 9,127)
( 10,128)( 11,133)( 12,134)( 13,131)( 14,132)( 15,137)( 16,138)( 17,135)
( 18,136)( 19,141)( 20,142)( 21,139)( 22,140)( 23,145)( 24,146)( 25,143)
( 26,144)( 27,149)( 28,150)( 29,147)( 30,148)( 31,153)( 32,154)( 33,151)
( 34,152)( 35,157)( 36,158)( 37,155)( 38,156)( 39,161)( 40,162)( 41,159)
( 42,160)( 43,165)( 44,166)( 45,163)( 46,164)( 47,169)( 48,170)( 49,167)
( 50,168)( 51,173)( 52,174)( 53,171)( 54,172)( 55,177)( 56,178)( 57,175)
( 58,176)( 59,181)( 60,182)( 61,179)( 62,180)( 63,185)( 64,186)( 65,183)
( 66,184)( 67,189)( 68,190)( 69,187)( 70,188)( 71,193)( 72,194)( 73,191)
( 74,192)( 75,197)( 76,198)( 77,195)( 78,196)( 79,201)( 80,202)( 81,199)
( 82,200)( 83,205)( 84,206)( 85,203)( 86,204)( 87,209)( 88,210)( 89,207)
( 90,208)( 91,213)( 92,214)( 93,211)( 94,212)( 95,217)( 96,218)( 97,215)
( 98,216)( 99,221)(100,222)(101,219)(102,220)(103,225)(104,226)(105,223)
(106,224)(107,229)(108,230)(109,227)(110,228)(111,233)(112,234)(113,231)
(114,232)(115,237)(116,238)(117,235)(118,236)(119,241)(120,242)(121,239)
(122,240);
s3 := Sym(242)!( 4, 5)( 7, 19)( 8, 21)( 9, 20)( 10, 22)( 11, 15)( 12, 17)
( 13, 16)( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)
( 29, 60)( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)
( 37, 52)( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)
( 68, 81)( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)
( 84,105)( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)
( 92,117)( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)
(100,109)(101,108)(102,110)(124,125)(127,139)(128,141)(129,140)(130,142)
(131,135)(132,137)(133,136)(134,138)(143,163)(144,165)(145,164)(146,166)
(147,179)(148,181)(149,180)(150,182)(151,175)(152,177)(153,176)(154,178)
(155,171)(156,173)(157,172)(158,174)(159,167)(160,169)(161,168)(162,170)
(184,185)(187,199)(188,201)(189,200)(190,202)(191,195)(192,197)(193,196)
(194,198)(203,223)(204,225)(205,224)(206,226)(207,239)(208,241)(209,240)
(210,242)(211,235)(212,237)(213,236)(214,238)(215,231)(216,233)(217,232)
(218,234)(219,227)(220,229)(221,228)(222,230);
s4 := Sym(242)!( 3, 47)( 4, 50)( 5, 49)( 6, 48)( 7, 43)( 8, 46)( 9, 45)
( 10, 44)( 11, 59)( 12, 62)( 13, 61)( 14, 60)( 15, 55)( 16, 58)( 17, 57)
( 18, 56)( 19, 51)( 20, 54)( 21, 53)( 22, 52)( 23, 27)( 24, 30)( 25, 29)
( 26, 28)( 31, 39)( 32, 42)( 33, 41)( 34, 40)( 36, 38)( 63,107)( 64,110)
( 65,109)( 66,108)( 67,103)( 68,106)( 69,105)( 70,104)( 71,119)( 72,122)
( 73,121)( 74,120)( 75,115)( 76,118)( 77,117)( 78,116)( 79,111)( 80,114)
( 81,113)( 82,112)( 83, 87)( 84, 90)( 85, 89)( 86, 88)( 91, 99)( 92,102)
( 93,101)( 94,100)( 96, 98)(123,167)(124,170)(125,169)(126,168)(127,163)
(128,166)(129,165)(130,164)(131,179)(132,182)(133,181)(134,180)(135,175)
(136,178)(137,177)(138,176)(139,171)(140,174)(141,173)(142,172)(143,147)
(144,150)(145,149)(146,148)(151,159)(152,162)(153,161)(154,160)(156,158)
(183,227)(184,230)(185,229)(186,228)(187,223)(188,226)(189,225)(190,224)
(191,239)(192,242)(193,241)(194,240)(195,235)(196,238)(197,237)(198,236)
(199,231)(200,234)(201,233)(202,232)(203,207)(204,210)(205,209)(206,208)
(211,219)(212,222)(213,221)(214,220)(216,218);
poly := sub<Sym(242)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope