Polytope of Type {12,4,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,10}*1920a
if this polytope has a name.
Group : SmallGroup(1920,151306)
Rank : 4
Schlafli Type : {12,4,10}
Number of vertices, edges, etc : 24, 48, 40, 10
Order of s0s1s2s3 : 60
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 : {12,4,10}*960
3-fold quotients : {4,4,10}*640
4-fold quotients : {12,2,10}*480, {6,4,10}*480
5-fold quotients : {12,4,2}*384a
6-fold quotients : {4,4,10}*320
8-fold quotients : {12,2,5}*240, {6,2,10}*240
10-fold quotients : {12,4,2}*192a
12-fold quotients : {2,4,10}*160, {4,2,10}*160
15-fold quotients : {4,4,2}*128
16-fold quotients : {3,2,10}*120, {6,2,5}*120
20-fold quotients : {12,2,2}*96, {6,4,2}*96a
24-fold quotients : {4,2,5}*80, {2,2,10}*80
30-fold quotients : {4,4,2}*64
32-fold quotients : {3,2,5}*60
40-fold quotients : {6,2,2}*48
48-fold quotients : {2,2,5}*40
60-fold quotients : {2,4,2}*32, {4,2,2}*32
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 := ( 1,121)( 2,122)( 3,123)( 4,124)( 5,125)( 6,131)( 7,132)( 8,133)
( 9,134)( 10,135)( 11,126)( 12,127)( 13,128)( 14,129)( 15,130)( 16,136)
( 17,137)( 18,138)( 19,139)( 20,140)( 21,146)( 22,147)( 23,148)( 24,149)
( 25,150)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,151)( 32,152)
( 33,153)( 34,154)( 35,155)( 36,161)( 37,162)( 38,163)( 39,164)( 40,165)
( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,166)( 47,167)( 48,168)
( 49,169)( 50,170)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)( 56,171)
( 57,172)( 58,173)( 59,174)( 60,175)( 61,181)( 62,182)( 63,183)( 64,184)
( 65,185)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,186)( 72,187)
( 73,188)( 74,189)( 75,190)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,206)( 82,207)( 83,208)( 84,209)( 85,210)( 86,201)( 87,202)( 88,203)
( 89,204)( 90,205)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,221)
( 97,222)( 98,223)( 99,224)(100,225)(101,216)(102,217)(103,218)(104,219)
(105,220)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)(112,237)
(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)(120,235);;
s1 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)( 18, 23)
( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 46, 51)
( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 66)( 62, 67)( 63, 68)( 64, 69)
( 65, 70)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91, 96)( 92, 97)
( 93, 98)( 94, 99)( 95,100)(106,111)(107,112)(108,113)(109,114)(110,115)
(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)
(129,154)(130,155)(131,161)(132,162)(133,163)(134,164)(135,165)(136,171)
(137,172)(138,173)(139,174)(140,175)(141,166)(142,167)(143,168)(144,169)
(145,170)(146,176)(147,177)(148,178)(149,179)(150,180)(181,216)(182,217)
(183,218)(184,219)(185,220)(186,211)(187,212)(188,213)(189,214)(190,215)
(191,221)(192,222)(193,223)(194,224)(195,225)(196,231)(197,232)(198,233)
(199,234)(200,235)(201,226)(202,227)(203,228)(204,229)(205,230)(206,236)
(207,237)(208,238)(209,239)(210,240);;
s2 := ( 1, 61)( 2, 65)( 3, 64)( 4, 63)( 5, 62)( 6, 66)( 7, 70)( 8, 69)
( 9, 68)( 10, 67)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)( 16, 76)
( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 81)( 22, 85)( 23, 84)( 24, 83)
( 25, 82)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31,106)( 32,110)
( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)( 39,113)( 40,112)
( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46, 91)( 47, 95)( 48, 94)
( 49, 93)( 50, 92)( 51, 96)( 52,100)( 53, 99)( 54, 98)( 55, 97)( 56,101)
( 57,105)( 58,104)( 59,103)( 60,102)(121,181)(122,185)(123,184)(124,183)
(125,182)(126,186)(127,190)(128,189)(129,188)(130,187)(131,191)(132,195)
(133,194)(134,193)(135,192)(136,196)(137,200)(138,199)(139,198)(140,197)
(141,201)(142,205)(143,204)(144,203)(145,202)(146,206)(147,210)(148,209)
(149,208)(150,207)(151,226)(152,230)(153,229)(154,228)(155,227)(156,231)
(157,235)(158,234)(159,233)(160,232)(161,236)(162,240)(163,239)(164,238)
(165,237)(166,211)(167,215)(168,214)(169,213)(170,212)(171,216)(172,220)
(173,219)(174,218)(175,217)(176,221)(177,225)(178,224)(179,223)(180,222);;
s3 := ( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 67)( 7, 66)( 8, 70)
( 9, 69)( 10, 68)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)( 16, 77)
( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 82)( 22, 81)( 23, 85)( 24, 84)
( 25, 83)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31, 92)( 32, 91)
( 33, 95)( 34, 94)( 35, 93)( 36, 97)( 37, 96)( 38,100)( 39, 99)( 40, 98)
( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,107)( 47,106)( 48,110)
( 49,109)( 50,108)( 51,112)( 52,111)( 53,115)( 54,114)( 55,113)( 56,117)
( 57,116)( 58,120)( 59,119)( 60,118)(121,182)(122,181)(123,185)(124,184)
(125,183)(126,187)(127,186)(128,190)(129,189)(130,188)(131,192)(132,191)
(133,195)(134,194)(135,193)(136,197)(137,196)(138,200)(139,199)(140,198)
(141,202)(142,201)(143,205)(144,204)(145,203)(146,207)(147,206)(148,210)
(149,209)(150,208)(151,212)(152,211)(153,215)(154,214)(155,213)(156,217)
(157,216)(158,220)(159,219)(160,218)(161,222)(162,221)(163,225)(164,224)
(165,223)(166,227)(167,226)(168,230)(169,229)(170,228)(171,232)(172,231)
(173,235)(174,234)(175,233)(176,237)(177,236)(178,240)(179,239)(180,238);;
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, s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(240)!( 1,121)( 2,122)( 3,123)( 4,124)( 5,125)( 6,131)( 7,132)
( 8,133)( 9,134)( 10,135)( 11,126)( 12,127)( 13,128)( 14,129)( 15,130)
( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,146)( 22,147)( 23,148)
( 24,149)( 25,150)( 26,141)( 27,142)( 28,143)( 29,144)( 30,145)( 31,151)
( 32,152)( 33,153)( 34,154)( 35,155)( 36,161)( 37,162)( 38,163)( 39,164)
( 40,165)( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,166)( 47,167)
( 48,168)( 49,169)( 50,170)( 51,176)( 52,177)( 53,178)( 54,179)( 55,180)
( 56,171)( 57,172)( 58,173)( 59,174)( 60,175)( 61,181)( 62,182)( 63,183)
( 64,184)( 65,185)( 66,191)( 67,192)( 68,193)( 69,194)( 70,195)( 71,186)
( 72,187)( 73,188)( 74,189)( 75,190)( 76,196)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,206)( 82,207)( 83,208)( 84,209)( 85,210)( 86,201)( 87,202)
( 88,203)( 89,204)( 90,205)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)
( 96,221)( 97,222)( 98,223)( 99,224)(100,225)(101,216)(102,217)(103,218)
(104,219)(105,220)(106,226)(107,227)(108,228)(109,229)(110,230)(111,236)
(112,237)(113,238)(114,239)(115,240)(116,231)(117,232)(118,233)(119,234)
(120,235);
s1 := Sym(240)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)
( 18, 23)( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)
( 46, 51)( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 66)( 62, 67)( 63, 68)
( 64, 69)( 65, 70)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91, 96)
( 92, 97)( 93, 98)( 94, 99)( 95,100)(106,111)(107,112)(108,113)(109,114)
(110,115)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)
(128,153)(129,154)(130,155)(131,161)(132,162)(133,163)(134,164)(135,165)
(136,171)(137,172)(138,173)(139,174)(140,175)(141,166)(142,167)(143,168)
(144,169)(145,170)(146,176)(147,177)(148,178)(149,179)(150,180)(181,216)
(182,217)(183,218)(184,219)(185,220)(186,211)(187,212)(188,213)(189,214)
(190,215)(191,221)(192,222)(193,223)(194,224)(195,225)(196,231)(197,232)
(198,233)(199,234)(200,235)(201,226)(202,227)(203,228)(204,229)(205,230)
(206,236)(207,237)(208,238)(209,239)(210,240);
s2 := Sym(240)!( 1, 61)( 2, 65)( 3, 64)( 4, 63)( 5, 62)( 6, 66)( 7, 70)
( 8, 69)( 9, 68)( 10, 67)( 11, 71)( 12, 75)( 13, 74)( 14, 73)( 15, 72)
( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 81)( 22, 85)( 23, 84)
( 24, 83)( 25, 82)( 26, 86)( 27, 90)( 28, 89)( 29, 88)( 30, 87)( 31,106)
( 32,110)( 33,109)( 34,108)( 35,107)( 36,111)( 37,115)( 38,114)( 39,113)
( 40,112)( 41,116)( 42,120)( 43,119)( 44,118)( 45,117)( 46, 91)( 47, 95)
( 48, 94)( 49, 93)( 50, 92)( 51, 96)( 52,100)( 53, 99)( 54, 98)( 55, 97)
( 56,101)( 57,105)( 58,104)( 59,103)( 60,102)(121,181)(122,185)(123,184)
(124,183)(125,182)(126,186)(127,190)(128,189)(129,188)(130,187)(131,191)
(132,195)(133,194)(134,193)(135,192)(136,196)(137,200)(138,199)(139,198)
(140,197)(141,201)(142,205)(143,204)(144,203)(145,202)(146,206)(147,210)
(148,209)(149,208)(150,207)(151,226)(152,230)(153,229)(154,228)(155,227)
(156,231)(157,235)(158,234)(159,233)(160,232)(161,236)(162,240)(163,239)
(164,238)(165,237)(166,211)(167,215)(168,214)(169,213)(170,212)(171,216)
(172,220)(173,219)(174,218)(175,217)(176,221)(177,225)(178,224)(179,223)
(180,222);
s3 := Sym(240)!( 1, 62)( 2, 61)( 3, 65)( 4, 64)( 5, 63)( 6, 67)( 7, 66)
( 8, 70)( 9, 69)( 10, 68)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)
( 16, 77)( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 82)( 22, 81)( 23, 85)
( 24, 84)( 25, 83)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31, 92)
( 32, 91)( 33, 95)( 34, 94)( 35, 93)( 36, 97)( 37, 96)( 38,100)( 39, 99)
( 40, 98)( 41,102)( 42,101)( 43,105)( 44,104)( 45,103)( 46,107)( 47,106)
( 48,110)( 49,109)( 50,108)( 51,112)( 52,111)( 53,115)( 54,114)( 55,113)
( 56,117)( 57,116)( 58,120)( 59,119)( 60,118)(121,182)(122,181)(123,185)
(124,184)(125,183)(126,187)(127,186)(128,190)(129,189)(130,188)(131,192)
(132,191)(133,195)(134,194)(135,193)(136,197)(137,196)(138,200)(139,199)
(140,198)(141,202)(142,201)(143,205)(144,204)(145,203)(146,207)(147,206)
(148,210)(149,209)(150,208)(151,212)(152,211)(153,215)(154,214)(155,213)
(156,217)(157,216)(158,220)(159,219)(160,218)(161,222)(162,221)(163,225)
(164,224)(165,223)(166,227)(167,226)(168,230)(169,229)(170,228)(171,232)
(172,231)(173,235)(174,234)(175,233)(176,237)(177,236)(178,240)(179,239)
(180,238);
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,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope