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