Polytope of Type {12,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,10}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240151)
Rank : 4
Schlafli Type : {12,4,10}
Number of vertices, edges, etc : 24, 48, 40, 10
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
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 : {6,4,10}*960
4-fold quotients : {3,4,10}*480
5-fold quotients : {12,4,2}*384c
8-fold quotients : {6,2,10}*240
10-fold quotients : {6,4,2}*192
16-fold quotients : {3,2,10}*120, {6,2,5}*120
20-fold quotients : {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
24-fold quotients : {2,2,10}*80
32-fold quotients : {3,2,5}*60
40-fold quotients : {3,4,2}*48, {6,2,2}*48
48-fold quotients : {2,2,5}*40
80-fold quotients : {3,2,2}*24
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)( 23, 44)
( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)( 31, 52)
( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)( 39, 60)
( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)( 82,102)
( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)( 90,110)
( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)( 98,118)
( 99,120)(100,119)(121,181)(122,182)(123,184)(124,183)(125,185)(126,186)
(127,188)(128,187)(129,189)(130,190)(131,192)(132,191)(133,193)(134,194)
(135,196)(136,195)(137,197)(138,198)(139,200)(140,199)(141,221)(142,222)
(143,224)(144,223)(145,225)(146,226)(147,228)(148,227)(149,229)(150,230)
(151,232)(152,231)(153,233)(154,234)(155,236)(156,235)(157,237)(158,238)
(159,240)(160,239)(161,201)(162,202)(163,204)(164,203)(165,205)(166,206)
(167,208)(168,207)(169,209)(170,210)(171,212)(172,211)(173,213)(174,214)
(175,216)(176,215)(177,217)(178,218)(179,220)(180,219);;
s1 := ( 1,141)( 2,144)( 3,143)( 4,142)( 5,145)( 6,148)( 7,147)( 8,146)
( 9,149)( 10,152)( 11,151)( 12,150)( 13,153)( 14,156)( 15,155)( 16,154)
( 17,157)( 18,160)( 19,159)( 20,158)( 21,121)( 22,124)( 23,123)( 24,122)
( 25,125)( 26,128)( 27,127)( 28,126)( 29,129)( 30,132)( 31,131)( 32,130)
( 33,133)( 34,136)( 35,135)( 36,134)( 37,137)( 38,140)( 39,139)( 40,138)
( 41,161)( 42,164)( 43,163)( 44,162)( 45,165)( 46,168)( 47,167)( 48,166)
( 49,169)( 50,172)( 51,171)( 52,170)( 53,173)( 54,176)( 55,175)( 56,174)
( 57,177)( 58,180)( 59,179)( 60,178)( 61,201)( 62,204)( 63,203)( 64,202)
( 65,205)( 66,208)( 67,207)( 68,206)( 69,209)( 70,212)( 71,211)( 72,210)
( 73,213)( 74,216)( 75,215)( 76,214)( 77,217)( 78,220)( 79,219)( 80,218)
( 81,181)( 82,184)( 83,183)( 84,182)( 85,185)( 86,188)( 87,187)( 88,186)
( 89,189)( 90,192)( 91,191)( 92,190)( 93,193)( 94,196)( 95,195)( 96,194)
( 97,197)( 98,200)( 99,199)(100,198)(101,221)(102,224)(103,223)(104,222)
(105,225)(106,228)(107,227)(108,226)(109,229)(110,232)(111,231)(112,230)
(113,233)(114,236)(115,235)(116,234)(117,237)(118,240)(119,239)(120,238);;
s2 := ( 1, 2)( 3, 4)( 5, 18)( 6, 17)( 7, 20)( 8, 19)( 9, 14)( 10, 13)
( 11, 16)( 12, 15)( 21, 22)( 23, 24)( 25, 38)( 26, 37)( 27, 40)( 28, 39)
( 29, 34)( 30, 33)( 31, 36)( 32, 35)( 41, 42)( 43, 44)( 45, 58)( 46, 57)
( 47, 60)( 48, 59)( 49, 54)( 50, 53)( 51, 56)( 52, 55)( 61, 62)( 63, 64)
( 65, 78)( 66, 77)( 67, 80)( 68, 79)( 69, 74)( 70, 73)( 71, 76)( 72, 75)
( 81, 82)( 83, 84)( 85, 98)( 86, 97)( 87,100)( 88, 99)( 89, 94)( 90, 93)
( 91, 96)( 92, 95)(101,102)(103,104)(105,118)(106,117)(107,120)(108,119)
(109,114)(110,113)(111,116)(112,115)(121,182)(122,181)(123,184)(124,183)
(125,198)(126,197)(127,200)(128,199)(129,194)(130,193)(131,196)(132,195)
(133,190)(134,189)(135,192)(136,191)(137,186)(138,185)(139,188)(140,187)
(141,202)(142,201)(143,204)(144,203)(145,218)(146,217)(147,220)(148,219)
(149,214)(150,213)(151,216)(152,215)(153,210)(154,209)(155,212)(156,211)
(157,206)(158,205)(159,208)(160,207)(161,222)(162,221)(163,224)(164,223)
(165,238)(166,237)(167,240)(168,239)(169,234)(170,233)(171,236)(172,235)
(173,230)(174,229)(175,232)(176,231)(177,226)(178,225)(179,228)(180,227);;
s3 := ( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9, 17)( 10, 18)( 11, 19)( 12, 20)
( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 29, 37)( 30, 38)( 31, 39)( 32, 40)
( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)
( 61, 65)( 62, 66)( 63, 67)( 64, 68)( 69, 77)( 70, 78)( 71, 79)( 72, 80)
( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 97)( 90, 98)( 91, 99)( 92,100)
(101,105)(102,106)(103,107)(104,108)(109,117)(110,118)(111,119)(112,120)
(121,125)(122,126)(123,127)(124,128)(129,137)(130,138)(131,139)(132,140)
(141,145)(142,146)(143,147)(144,148)(149,157)(150,158)(151,159)(152,160)
(161,165)(162,166)(163,167)(164,168)(169,177)(170,178)(171,179)(172,180)
(181,185)(182,186)(183,187)(184,188)(189,197)(190,198)(191,199)(192,200)
(201,205)(202,206)(203,207)(204,208)(209,217)(210,218)(211,219)(212,220)
(221,225)(222,226)(223,227)(224,228)(229,237)(230,238)(231,239)(232,240);;
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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
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(240)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 19, 20)( 21, 41)( 22, 42)
( 23, 44)( 24, 43)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 49)( 30, 50)
( 31, 52)( 32, 51)( 33, 53)( 34, 54)( 35, 56)( 36, 55)( 37, 57)( 38, 58)
( 39, 60)( 40, 59)( 63, 64)( 67, 68)( 71, 72)( 75, 76)( 79, 80)( 81,101)
( 82,102)( 83,104)( 84,103)( 85,105)( 86,106)( 87,108)( 88,107)( 89,109)
( 90,110)( 91,112)( 92,111)( 93,113)( 94,114)( 95,116)( 96,115)( 97,117)
( 98,118)( 99,120)(100,119)(121,181)(122,182)(123,184)(124,183)(125,185)
(126,186)(127,188)(128,187)(129,189)(130,190)(131,192)(132,191)(133,193)
(134,194)(135,196)(136,195)(137,197)(138,198)(139,200)(140,199)(141,221)
(142,222)(143,224)(144,223)(145,225)(146,226)(147,228)(148,227)(149,229)
(150,230)(151,232)(152,231)(153,233)(154,234)(155,236)(156,235)(157,237)
(158,238)(159,240)(160,239)(161,201)(162,202)(163,204)(164,203)(165,205)
(166,206)(167,208)(168,207)(169,209)(170,210)(171,212)(172,211)(173,213)
(174,214)(175,216)(176,215)(177,217)(178,218)(179,220)(180,219);
s1 := Sym(240)!( 1,141)( 2,144)( 3,143)( 4,142)( 5,145)( 6,148)( 7,147)
( 8,146)( 9,149)( 10,152)( 11,151)( 12,150)( 13,153)( 14,156)( 15,155)
( 16,154)( 17,157)( 18,160)( 19,159)( 20,158)( 21,121)( 22,124)( 23,123)
( 24,122)( 25,125)( 26,128)( 27,127)( 28,126)( 29,129)( 30,132)( 31,131)
( 32,130)( 33,133)( 34,136)( 35,135)( 36,134)( 37,137)( 38,140)( 39,139)
( 40,138)( 41,161)( 42,164)( 43,163)( 44,162)( 45,165)( 46,168)( 47,167)
( 48,166)( 49,169)( 50,172)( 51,171)( 52,170)( 53,173)( 54,176)( 55,175)
( 56,174)( 57,177)( 58,180)( 59,179)( 60,178)( 61,201)( 62,204)( 63,203)
( 64,202)( 65,205)( 66,208)( 67,207)( 68,206)( 69,209)( 70,212)( 71,211)
( 72,210)( 73,213)( 74,216)( 75,215)( 76,214)( 77,217)( 78,220)( 79,219)
( 80,218)( 81,181)( 82,184)( 83,183)( 84,182)( 85,185)( 86,188)( 87,187)
( 88,186)( 89,189)( 90,192)( 91,191)( 92,190)( 93,193)( 94,196)( 95,195)
( 96,194)( 97,197)( 98,200)( 99,199)(100,198)(101,221)(102,224)(103,223)
(104,222)(105,225)(106,228)(107,227)(108,226)(109,229)(110,232)(111,231)
(112,230)(113,233)(114,236)(115,235)(116,234)(117,237)(118,240)(119,239)
(120,238);
s2 := Sym(240)!( 1, 2)( 3, 4)( 5, 18)( 6, 17)( 7, 20)( 8, 19)( 9, 14)
( 10, 13)( 11, 16)( 12, 15)( 21, 22)( 23, 24)( 25, 38)( 26, 37)( 27, 40)
( 28, 39)( 29, 34)( 30, 33)( 31, 36)( 32, 35)( 41, 42)( 43, 44)( 45, 58)
( 46, 57)( 47, 60)( 48, 59)( 49, 54)( 50, 53)( 51, 56)( 52, 55)( 61, 62)
( 63, 64)( 65, 78)( 66, 77)( 67, 80)( 68, 79)( 69, 74)( 70, 73)( 71, 76)
( 72, 75)( 81, 82)( 83, 84)( 85, 98)( 86, 97)( 87,100)( 88, 99)( 89, 94)
( 90, 93)( 91, 96)( 92, 95)(101,102)(103,104)(105,118)(106,117)(107,120)
(108,119)(109,114)(110,113)(111,116)(112,115)(121,182)(122,181)(123,184)
(124,183)(125,198)(126,197)(127,200)(128,199)(129,194)(130,193)(131,196)
(132,195)(133,190)(134,189)(135,192)(136,191)(137,186)(138,185)(139,188)
(140,187)(141,202)(142,201)(143,204)(144,203)(145,218)(146,217)(147,220)
(148,219)(149,214)(150,213)(151,216)(152,215)(153,210)(154,209)(155,212)
(156,211)(157,206)(158,205)(159,208)(160,207)(161,222)(162,221)(163,224)
(164,223)(165,238)(166,237)(167,240)(168,239)(169,234)(170,233)(171,236)
(172,235)(173,230)(174,229)(175,232)(176,231)(177,226)(178,225)(179,228)
(180,227);
s3 := Sym(240)!( 1, 5)( 2, 6)( 3, 7)( 4, 8)( 9, 17)( 10, 18)( 11, 19)
( 12, 20)( 21, 25)( 22, 26)( 23, 27)( 24, 28)( 29, 37)( 30, 38)( 31, 39)
( 32, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 57)( 50, 58)( 51, 59)
( 52, 60)( 61, 65)( 62, 66)( 63, 67)( 64, 68)( 69, 77)( 70, 78)( 71, 79)
( 72, 80)( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 97)( 90, 98)( 91, 99)
( 92,100)(101,105)(102,106)(103,107)(104,108)(109,117)(110,118)(111,119)
(112,120)(121,125)(122,126)(123,127)(124,128)(129,137)(130,138)(131,139)
(132,140)(141,145)(142,146)(143,147)(144,148)(149,157)(150,158)(151,159)
(152,160)(161,165)(162,166)(163,167)(164,168)(169,177)(170,178)(171,179)
(172,180)(181,185)(182,186)(183,187)(184,188)(189,197)(190,198)(191,199)
(192,200)(201,205)(202,206)(203,207)(204,208)(209,217)(210,218)(211,219)
(212,220)(221,225)(222,226)(223,227)(224,228)(229,237)(230,238)(231,239)
(232,240);
poly := sub<Sym(240)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope