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