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