Polytope of Type {2,10,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,12,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240141)
Rank : 5
Schlafli Type : {2,10,12,4}
Number of vertices, edges, etc : 2, 10, 60, 24, 4
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 : {2,10,6,4}*960b
5-fold quotients : {2,2,12,4}*384b
10-fold quotients : {2,2,6,4}*192c
20-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 7, 19)( 8, 20)( 9, 21)( 10, 22)( 11, 15)( 12, 16)( 13, 17)( 14, 18)
( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 35)( 32, 36)( 33, 37)( 34, 38)
( 47, 59)( 48, 60)( 49, 61)( 50, 62)( 51, 55)( 52, 56)( 53, 57)( 54, 58)
( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)( 74, 78)
( 87, 99)( 88,100)( 89,101)( 90,102)( 91, 95)( 92, 96)( 93, 97)( 94, 98)
(107,119)(108,120)(109,121)(110,122)(111,115)(112,116)(113,117)(114,118)
(127,139)(128,140)(129,141)(130,142)(131,135)(132,136)(133,137)(134,138)
(147,159)(148,160)(149,161)(150,162)(151,155)(152,156)(153,157)(154,158)
(167,179)(168,180)(169,181)(170,182)(171,175)(172,176)(173,177)(174,178)
(187,199)(188,200)(189,201)(190,202)(191,195)(192,196)(193,197)(194,198)
(207,219)(208,220)(209,221)(210,222)(211,215)(212,216)(213,217)(214,218)
(227,239)(228,240)(229,241)(230,242)(231,235)(232,236)(233,237)(234,238);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6, 10)( 11, 19)( 12, 21)( 13, 20)( 14, 22)
( 16, 17)( 23, 47)( 24, 49)( 25, 48)( 26, 50)( 27, 43)( 28, 45)( 29, 44)
( 30, 46)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 55)( 36, 57)( 37, 56)
( 38, 58)( 39, 51)( 40, 53)( 41, 52)( 42, 54)( 63, 67)( 64, 69)( 65, 68)
( 66, 70)( 71, 79)( 72, 81)( 73, 80)( 74, 82)( 76, 77)( 83,107)( 84,109)
( 85,108)( 86,110)( 87,103)( 88,105)( 89,104)( 90,106)( 91,119)( 92,121)
( 93,120)( 94,122)( 95,115)( 96,117)( 97,116)( 98,118)( 99,111)(100,113)
(101,112)(102,114)(123,187)(124,189)(125,188)(126,190)(127,183)(128,185)
(129,184)(130,186)(131,199)(132,201)(133,200)(134,202)(135,195)(136,197)
(137,196)(138,198)(139,191)(140,193)(141,192)(142,194)(143,227)(144,229)
(145,228)(146,230)(147,223)(148,225)(149,224)(150,226)(151,239)(152,241)
(153,240)(154,242)(155,235)(156,237)(157,236)(158,238)(159,231)(160,233)
(161,232)(162,234)(163,207)(164,209)(165,208)(166,210)(167,203)(168,205)
(169,204)(170,206)(171,219)(172,221)(173,220)(174,222)(175,215)(176,217)
(177,216)(178,218)(179,211)(180,213)(181,212)(182,214);;
s3 := ( 3,143)( 4,144)( 5,146)( 6,145)( 7,147)( 8,148)( 9,150)( 10,149)
( 11,151)( 12,152)( 13,154)( 14,153)( 15,155)( 16,156)( 17,158)( 18,157)
( 19,159)( 20,160)( 21,162)( 22,161)( 23,123)( 24,124)( 25,126)( 26,125)
( 27,127)( 28,128)( 29,130)( 30,129)( 31,131)( 32,132)( 33,134)( 34,133)
( 35,135)( 36,136)( 37,138)( 38,137)( 39,139)( 40,140)( 41,142)( 42,141)
( 43,163)( 44,164)( 45,166)( 46,165)( 47,167)( 48,168)( 49,170)( 50,169)
( 51,171)( 52,172)( 53,174)( 54,173)( 55,175)( 56,176)( 57,178)( 58,177)
( 59,179)( 60,180)( 61,182)( 62,181)( 63,203)( 64,204)( 65,206)( 66,205)
( 67,207)( 68,208)( 69,210)( 70,209)( 71,211)( 72,212)( 73,214)( 74,213)
( 75,215)( 76,216)( 77,218)( 78,217)( 79,219)( 80,220)( 81,222)( 82,221)
( 83,183)( 84,184)( 85,186)( 86,185)( 87,187)( 88,188)( 89,190)( 90,189)
( 91,191)( 92,192)( 93,194)( 94,193)( 95,195)( 96,196)( 97,198)( 98,197)
( 99,199)(100,200)(101,202)(102,201)(103,223)(104,224)(105,226)(106,225)
(107,227)(108,228)(109,230)(110,229)(111,231)(112,232)(113,234)(114,233)
(115,235)(116,236)(117,238)(118,237)(119,239)(120,240)(121,242)(122,241);;
s4 := ( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)( 16, 17)
( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)( 32, 33)
( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)( 48, 49)
( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)( 64, 65)
( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)( 80, 81)
( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)( 96, 97)
( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)(112,113)
(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)(128,129)
(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)(144,145)
(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)(160,161)
(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)(176,177)
(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)(192,193)
(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)(208,209)
(211,214)(212,213)(215,218)(216,217)(219,222)(220,221)(223,226)(224,225)
(227,230)(228,229)(231,234)(232,233)(235,238)(236,237)(239,242)(240,241);;
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*s3*s2*s1*s2*s3*s2, s3*s4*s3*s4*s3*s4*s3*s4,
s4*s3*s2*s4*s3*s4*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!(1,2);
s1 := Sym(242)!( 7, 19)( 8, 20)( 9, 21)( 10, 22)( 11, 15)( 12, 16)( 13, 17)
( 14, 18)( 27, 39)( 28, 40)( 29, 41)( 30, 42)( 31, 35)( 32, 36)( 33, 37)
( 34, 38)( 47, 59)( 48, 60)( 49, 61)( 50, 62)( 51, 55)( 52, 56)( 53, 57)
( 54, 58)( 67, 79)( 68, 80)( 69, 81)( 70, 82)( 71, 75)( 72, 76)( 73, 77)
( 74, 78)( 87, 99)( 88,100)( 89,101)( 90,102)( 91, 95)( 92, 96)( 93, 97)
( 94, 98)(107,119)(108,120)(109,121)(110,122)(111,115)(112,116)(113,117)
(114,118)(127,139)(128,140)(129,141)(130,142)(131,135)(132,136)(133,137)
(134,138)(147,159)(148,160)(149,161)(150,162)(151,155)(152,156)(153,157)
(154,158)(167,179)(168,180)(169,181)(170,182)(171,175)(172,176)(173,177)
(174,178)(187,199)(188,200)(189,201)(190,202)(191,195)(192,196)(193,197)
(194,198)(207,219)(208,220)(209,221)(210,222)(211,215)(212,216)(213,217)
(214,218)(227,239)(228,240)(229,241)(230,242)(231,235)(232,236)(233,237)
(234,238);
s2 := Sym(242)!( 3, 7)( 4, 9)( 5, 8)( 6, 10)( 11, 19)( 12, 21)( 13, 20)
( 14, 22)( 16, 17)( 23, 47)( 24, 49)( 25, 48)( 26, 50)( 27, 43)( 28, 45)
( 29, 44)( 30, 46)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 55)( 36, 57)
( 37, 56)( 38, 58)( 39, 51)( 40, 53)( 41, 52)( 42, 54)( 63, 67)( 64, 69)
( 65, 68)( 66, 70)( 71, 79)( 72, 81)( 73, 80)( 74, 82)( 76, 77)( 83,107)
( 84,109)( 85,108)( 86,110)( 87,103)( 88,105)( 89,104)( 90,106)( 91,119)
( 92,121)( 93,120)( 94,122)( 95,115)( 96,117)( 97,116)( 98,118)( 99,111)
(100,113)(101,112)(102,114)(123,187)(124,189)(125,188)(126,190)(127,183)
(128,185)(129,184)(130,186)(131,199)(132,201)(133,200)(134,202)(135,195)
(136,197)(137,196)(138,198)(139,191)(140,193)(141,192)(142,194)(143,227)
(144,229)(145,228)(146,230)(147,223)(148,225)(149,224)(150,226)(151,239)
(152,241)(153,240)(154,242)(155,235)(156,237)(157,236)(158,238)(159,231)
(160,233)(161,232)(162,234)(163,207)(164,209)(165,208)(166,210)(167,203)
(168,205)(169,204)(170,206)(171,219)(172,221)(173,220)(174,222)(175,215)
(176,217)(177,216)(178,218)(179,211)(180,213)(181,212)(182,214);
s3 := Sym(242)!( 3,143)( 4,144)( 5,146)( 6,145)( 7,147)( 8,148)( 9,150)
( 10,149)( 11,151)( 12,152)( 13,154)( 14,153)( 15,155)( 16,156)( 17,158)
( 18,157)( 19,159)( 20,160)( 21,162)( 22,161)( 23,123)( 24,124)( 25,126)
( 26,125)( 27,127)( 28,128)( 29,130)( 30,129)( 31,131)( 32,132)( 33,134)
( 34,133)( 35,135)( 36,136)( 37,138)( 38,137)( 39,139)( 40,140)( 41,142)
( 42,141)( 43,163)( 44,164)( 45,166)( 46,165)( 47,167)( 48,168)( 49,170)
( 50,169)( 51,171)( 52,172)( 53,174)( 54,173)( 55,175)( 56,176)( 57,178)
( 58,177)( 59,179)( 60,180)( 61,182)( 62,181)( 63,203)( 64,204)( 65,206)
( 66,205)( 67,207)( 68,208)( 69,210)( 70,209)( 71,211)( 72,212)( 73,214)
( 74,213)( 75,215)( 76,216)( 77,218)( 78,217)( 79,219)( 80,220)( 81,222)
( 82,221)( 83,183)( 84,184)( 85,186)( 86,185)( 87,187)( 88,188)( 89,190)
( 90,189)( 91,191)( 92,192)( 93,194)( 94,193)( 95,195)( 96,196)( 97,198)
( 98,197)( 99,199)(100,200)(101,202)(102,201)(103,223)(104,224)(105,226)
(106,225)(107,227)(108,228)(109,230)(110,229)(111,231)(112,232)(113,234)
(114,233)(115,235)(116,236)(117,238)(118,237)(119,239)(120,240)(121,242)
(122,241);
s4 := Sym(242)!( 3, 6)( 4, 5)( 7, 10)( 8, 9)( 11, 14)( 12, 13)( 15, 18)
( 16, 17)( 19, 22)( 20, 21)( 23, 26)( 24, 25)( 27, 30)( 28, 29)( 31, 34)
( 32, 33)( 35, 38)( 36, 37)( 39, 42)( 40, 41)( 43, 46)( 44, 45)( 47, 50)
( 48, 49)( 51, 54)( 52, 53)( 55, 58)( 56, 57)( 59, 62)( 60, 61)( 63, 66)
( 64, 65)( 67, 70)( 68, 69)( 71, 74)( 72, 73)( 75, 78)( 76, 77)( 79, 82)
( 80, 81)( 83, 86)( 84, 85)( 87, 90)( 88, 89)( 91, 94)( 92, 93)( 95, 98)
( 96, 97)( 99,102)(100,101)(103,106)(104,105)(107,110)(108,109)(111,114)
(112,113)(115,118)(116,117)(119,122)(120,121)(123,126)(124,125)(127,130)
(128,129)(131,134)(132,133)(135,138)(136,137)(139,142)(140,141)(143,146)
(144,145)(147,150)(148,149)(151,154)(152,153)(155,158)(156,157)(159,162)
(160,161)(163,166)(164,165)(167,170)(168,169)(171,174)(172,173)(175,178)
(176,177)(179,182)(180,181)(183,186)(184,185)(187,190)(188,189)(191,194)
(192,193)(195,198)(196,197)(199,202)(200,201)(203,206)(204,205)(207,210)
(208,209)(211,214)(212,213)(215,218)(216,217)(219,222)(220,221)(223,226)
(224,225)(227,230)(228,229)(231,234)(232,233)(235,238)(236,237)(239,242)
(240,241);
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*s3*s2*s1*s2*s3*s2,
s3*s4*s3*s4*s3*s4*s3*s4, s4*s3*s2*s4*s3*s4*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 >;
to this polytope