Polytope of Type {2,2,4,60}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,60}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240289)
Rank : 5
Schlafli Type : {2,2,4,60}
Number of vertices, edges, etc : 2, 2, 4, 120, 60
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-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 : {2,2,4,30}*960b
4-fold quotients : {2,2,4,15}*480
5-fold quotients : {2,2,4,12}*384b
10-fold quotients : {2,2,4,6}*192c
20-fold quotients : {2,2,4,3}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)
( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)
( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)
( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)
( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)
( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)
(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)
(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)
(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)
(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)
(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)
(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)
(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)
(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)
(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)(242,244);;
s3 := ( 6, 7)( 9, 21)( 10, 23)( 11, 22)( 12, 24)( 13, 17)( 14, 19)( 15, 18)
( 16, 20)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 61)( 30, 63)( 31, 62)
( 32, 64)( 33, 57)( 34, 59)( 35, 58)( 36, 60)( 37, 53)( 38, 55)( 39, 54)
( 40, 56)( 41, 49)( 42, 51)( 43, 50)( 44, 52)( 66, 67)( 69, 81)( 70, 83)
( 71, 82)( 72, 84)( 73, 77)( 74, 79)( 75, 78)( 76, 80)( 85,105)( 86,107)
( 87,106)( 88,108)( 89,121)( 90,123)( 91,122)( 92,124)( 93,117)( 94,119)
( 95,118)( 96,120)( 97,113)( 98,115)( 99,114)(100,116)(101,109)(102,111)
(103,110)(104,112)(125,185)(126,187)(127,186)(128,188)(129,201)(130,203)
(131,202)(132,204)(133,197)(134,199)(135,198)(136,200)(137,193)(138,195)
(139,194)(140,196)(141,189)(142,191)(143,190)(144,192)(145,225)(146,227)
(147,226)(148,228)(149,241)(150,243)(151,242)(152,244)(153,237)(154,239)
(155,238)(156,240)(157,233)(158,235)(159,234)(160,236)(161,229)(162,231)
(163,230)(164,232)(165,205)(166,207)(167,206)(168,208)(169,221)(170,223)
(171,222)(172,224)(173,217)(174,219)(175,218)(176,220)(177,213)(178,215)
(179,214)(180,216)(181,209)(182,211)(183,210)(184,212);;
s4 := ( 5,169)( 6,172)( 7,171)( 8,170)( 9,165)( 10,168)( 11,167)( 12,166)
( 13,181)( 14,184)( 15,183)( 16,182)( 17,177)( 18,180)( 19,179)( 20,178)
( 21,173)( 22,176)( 23,175)( 24,174)( 25,149)( 26,152)( 27,151)( 28,150)
( 29,145)( 30,148)( 31,147)( 32,146)( 33,161)( 34,164)( 35,163)( 36,162)
( 37,157)( 38,160)( 39,159)( 40,158)( 41,153)( 42,156)( 43,155)( 44,154)
( 45,129)( 46,132)( 47,131)( 48,130)( 49,125)( 50,128)( 51,127)( 52,126)
( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)
( 61,133)( 62,136)( 63,135)( 64,134)( 65,229)( 66,232)( 67,231)( 68,230)
( 69,225)( 70,228)( 71,227)( 72,226)( 73,241)( 74,244)( 75,243)( 76,242)
( 77,237)( 78,240)( 79,239)( 80,238)( 81,233)( 82,236)( 83,235)( 84,234)
( 85,209)( 86,212)( 87,211)( 88,210)( 89,205)( 90,208)( 91,207)( 92,206)
( 93,221)( 94,224)( 95,223)( 96,222)( 97,217)( 98,220)( 99,219)(100,218)
(101,213)(102,216)(103,215)(104,214)(105,189)(106,192)(107,191)(108,190)
(109,185)(110,188)(111,187)(112,186)(113,201)(114,204)(115,203)(116,202)
(117,197)(118,200)(119,199)(120,198)(121,193)(122,196)(123,195)(124,194);;
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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s4*s2*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*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*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*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(244)!(1,2);
s1 := Sym(244)!(3,4);
s2 := Sym(244)!( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)
( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)
( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)
( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)
( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)
( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)
( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)
(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)
(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)
(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)
(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)
(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)
(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)
(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)
(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)
(242,244);
s3 := Sym(244)!( 6, 7)( 9, 21)( 10, 23)( 11, 22)( 12, 24)( 13, 17)( 14, 19)
( 15, 18)( 16, 20)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 61)( 30, 63)
( 31, 62)( 32, 64)( 33, 57)( 34, 59)( 35, 58)( 36, 60)( 37, 53)( 38, 55)
( 39, 54)( 40, 56)( 41, 49)( 42, 51)( 43, 50)( 44, 52)( 66, 67)( 69, 81)
( 70, 83)( 71, 82)( 72, 84)( 73, 77)( 74, 79)( 75, 78)( 76, 80)( 85,105)
( 86,107)( 87,106)( 88,108)( 89,121)( 90,123)( 91,122)( 92,124)( 93,117)
( 94,119)( 95,118)( 96,120)( 97,113)( 98,115)( 99,114)(100,116)(101,109)
(102,111)(103,110)(104,112)(125,185)(126,187)(127,186)(128,188)(129,201)
(130,203)(131,202)(132,204)(133,197)(134,199)(135,198)(136,200)(137,193)
(138,195)(139,194)(140,196)(141,189)(142,191)(143,190)(144,192)(145,225)
(146,227)(147,226)(148,228)(149,241)(150,243)(151,242)(152,244)(153,237)
(154,239)(155,238)(156,240)(157,233)(158,235)(159,234)(160,236)(161,229)
(162,231)(163,230)(164,232)(165,205)(166,207)(167,206)(168,208)(169,221)
(170,223)(171,222)(172,224)(173,217)(174,219)(175,218)(176,220)(177,213)
(178,215)(179,214)(180,216)(181,209)(182,211)(183,210)(184,212);
s4 := Sym(244)!( 5,169)( 6,172)( 7,171)( 8,170)( 9,165)( 10,168)( 11,167)
( 12,166)( 13,181)( 14,184)( 15,183)( 16,182)( 17,177)( 18,180)( 19,179)
( 20,178)( 21,173)( 22,176)( 23,175)( 24,174)( 25,149)( 26,152)( 27,151)
( 28,150)( 29,145)( 30,148)( 31,147)( 32,146)( 33,161)( 34,164)( 35,163)
( 36,162)( 37,157)( 38,160)( 39,159)( 40,158)( 41,153)( 42,156)( 43,155)
( 44,154)( 45,129)( 46,132)( 47,131)( 48,130)( 49,125)( 50,128)( 51,127)
( 52,126)( 53,141)( 54,144)( 55,143)( 56,142)( 57,137)( 58,140)( 59,139)
( 60,138)( 61,133)( 62,136)( 63,135)( 64,134)( 65,229)( 66,232)( 67,231)
( 68,230)( 69,225)( 70,228)( 71,227)( 72,226)( 73,241)( 74,244)( 75,243)
( 76,242)( 77,237)( 78,240)( 79,239)( 80,238)( 81,233)( 82,236)( 83,235)
( 84,234)( 85,209)( 86,212)( 87,211)( 88,210)( 89,205)( 90,208)( 91,207)
( 92,206)( 93,221)( 94,224)( 95,223)( 96,222)( 97,217)( 98,220)( 99,219)
(100,218)(101,213)(102,216)(103,215)(104,214)(105,189)(106,192)(107,191)
(108,190)(109,185)(110,188)(111,187)(112,186)(113,201)(114,204)(115,203)
(116,202)(117,197)(118,200)(119,199)(120,198)(121,193)(122,196)(123,195)
(124,194);
poly := sub<Sym(244)|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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*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*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*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*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