Polytope of Type {2,4,10,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,10,12}*1920
if this polytope has a name.
Group : SmallGroup(1920,208134)
Rank : 5
Schlafli Type : {2,4,10,12}
Number of vertices, edges, etc : 2, 4, 20, 60, 12
Order of s0s1s2s3s4 : 60
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
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 : {2,2,10,12}*960, {2,4,10,6}*960
3-fold quotients : {2,4,10,4}*640
4-fold quotients : {2,2,10,6}*480
5-fold quotients : {2,4,2,12}*384
6-fold quotients : {2,2,10,4}*320, {2,4,10,2}*320
10-fold quotients : {2,2,2,12}*192, {2,4,2,6}*192
12-fold quotients : {2,2,10,2}*160
15-fold quotients : {2,4,2,4}*128
20-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
24-fold quotients : {2,2,5,2}*80
30-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
40-fold quotients : {2,2,2,3}*48
60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,123)( 4,124)( 5,125)( 6,126)( 7,127)( 8,128)( 9,129)( 10,130)
( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)( 18,138)
( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)( 26,146)
( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)( 34,154)
( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)( 42,162)
( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)( 50,170)
( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)
( 59,179)( 60,180)( 61,181)( 62,182)( 63,198)( 64,199)( 65,200)( 66,201)
( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)( 72,207)( 73,208)( 74,209)
( 75,210)( 76,211)( 77,212)( 78,183)( 79,184)( 80,185)( 81,186)( 82,187)
( 83,188)( 84,189)( 85,190)( 86,191)( 87,192)( 88,193)( 89,194)( 90,195)
( 91,196)( 92,197)( 93,228)( 94,229)( 95,230)( 96,231)( 97,232)( 98,233)
( 99,234)(100,235)(101,236)(102,237)(103,238)(104,239)(105,240)(106,241)
(107,242)(108,213)(109,214)(110,215)(111,216)(112,217)(113,218)(114,219)
(115,220)(116,221)(117,222)(118,223)(119,224)(120,225)(121,226)(122,227);;
s2 := ( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)( 60, 61)
( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)( 80, 81)
( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101)
(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)(120,121)
(123,138)(124,142)(125,141)(126,140)(127,139)(128,143)(129,147)(130,146)
(131,145)(132,144)(133,148)(134,152)(135,151)(136,150)(137,149)(153,168)
(154,172)(155,171)(156,170)(157,169)(158,173)(159,177)(160,176)(161,175)
(162,174)(163,178)(164,182)(165,181)(166,180)(167,179)(183,198)(184,202)
(185,201)(186,200)(187,199)(188,203)(189,207)(190,206)(191,205)(192,204)
(193,208)(194,212)(195,211)(196,210)(197,209)(213,228)(214,232)(215,231)
(216,230)(217,229)(218,233)(219,237)(220,236)(221,235)(222,234)(223,238)
(224,242)(225,241)(226,240)(227,239);;
s3 := ( 3, 64)( 4, 63)( 5, 67)( 6, 66)( 7, 65)( 8, 74)( 9, 73)( 10, 77)
( 11, 76)( 12, 75)( 13, 69)( 14, 68)( 15, 72)( 16, 71)( 17, 70)( 18, 79)
( 19, 78)( 20, 82)( 21, 81)( 22, 80)( 23, 89)( 24, 88)( 25, 92)( 26, 91)
( 27, 90)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 94)( 34, 93)
( 35, 97)( 36, 96)( 37, 95)( 38,104)( 39,103)( 40,107)( 41,106)( 42,105)
( 43, 99)( 44, 98)( 45,102)( 46,101)( 47,100)( 48,109)( 49,108)( 50,112)
( 51,111)( 52,110)( 53,119)( 54,118)( 55,122)( 56,121)( 57,120)( 58,114)
( 59,113)( 60,117)( 61,116)( 62,115)(123,199)(124,198)(125,202)(126,201)
(127,200)(128,209)(129,208)(130,212)(131,211)(132,210)(133,204)(134,203)
(135,207)(136,206)(137,205)(138,184)(139,183)(140,187)(141,186)(142,185)
(143,194)(144,193)(145,197)(146,196)(147,195)(148,189)(149,188)(150,192)
(151,191)(152,190)(153,229)(154,228)(155,232)(156,231)(157,230)(158,239)
(159,238)(160,242)(161,241)(162,240)(163,234)(164,233)(165,237)(166,236)
(167,235)(168,214)(169,213)(170,217)(171,216)(172,215)(173,224)(174,223)
(175,227)(176,226)(177,225)(178,219)(179,218)(180,222)(181,221)(182,220);;
s4 := ( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)( 20, 25)
( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)( 48, 53)
( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 98)( 64, 99)( 65,100)( 66,101)
( 67,102)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)( 73,103)( 74,104)
( 75,105)( 76,106)( 77,107)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)
( 83,108)( 84,109)( 85,110)( 86,111)( 87,112)( 88,118)( 89,119)( 90,120)
( 91,121)( 92,122)(123,128)(124,129)(125,130)(126,131)(127,132)(138,143)
(139,144)(140,145)(141,146)(142,147)(153,158)(154,159)(155,160)(156,161)
(157,162)(168,173)(169,174)(170,175)(171,176)(172,177)(183,218)(184,219)
(185,220)(186,221)(187,222)(188,213)(189,214)(190,215)(191,216)(192,217)
(193,223)(194,224)(195,225)(196,226)(197,227)(198,233)(199,234)(200,235)
(201,236)(202,237)(203,228)(204,229)(205,230)(206,231)(207,232)(208,238)
(209,239)(210,240)(211,241)(212,242);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*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)!( 3,123)( 4,124)( 5,125)( 6,126)( 7,127)( 8,128)( 9,129)
( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)
( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)
( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)
( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)
( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)
( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)
( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,198)( 64,199)( 65,200)
( 66,201)( 67,202)( 68,203)( 69,204)( 70,205)( 71,206)( 72,207)( 73,208)
( 74,209)( 75,210)( 76,211)( 77,212)( 78,183)( 79,184)( 80,185)( 81,186)
( 82,187)( 83,188)( 84,189)( 85,190)( 86,191)( 87,192)( 88,193)( 89,194)
( 90,195)( 91,196)( 92,197)( 93,228)( 94,229)( 95,230)( 96,231)( 97,232)
( 98,233)( 99,234)(100,235)(101,236)(102,237)(103,238)(104,239)(105,240)
(106,241)(107,242)(108,213)(109,214)(110,215)(111,216)(112,217)(113,218)
(114,219)(115,220)(116,221)(117,222)(118,223)(119,224)(120,225)(121,226)
(122,227);
s2 := Sym(242)!( 4, 7)( 5, 6)( 9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)
( 60, 61)( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)
( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)
(100,101)(104,107)(105,106)(109,112)(110,111)(114,117)(115,116)(119,122)
(120,121)(123,138)(124,142)(125,141)(126,140)(127,139)(128,143)(129,147)
(130,146)(131,145)(132,144)(133,148)(134,152)(135,151)(136,150)(137,149)
(153,168)(154,172)(155,171)(156,170)(157,169)(158,173)(159,177)(160,176)
(161,175)(162,174)(163,178)(164,182)(165,181)(166,180)(167,179)(183,198)
(184,202)(185,201)(186,200)(187,199)(188,203)(189,207)(190,206)(191,205)
(192,204)(193,208)(194,212)(195,211)(196,210)(197,209)(213,228)(214,232)
(215,231)(216,230)(217,229)(218,233)(219,237)(220,236)(221,235)(222,234)
(223,238)(224,242)(225,241)(226,240)(227,239);
s3 := Sym(242)!( 3, 64)( 4, 63)( 5, 67)( 6, 66)( 7, 65)( 8, 74)( 9, 73)
( 10, 77)( 11, 76)( 12, 75)( 13, 69)( 14, 68)( 15, 72)( 16, 71)( 17, 70)
( 18, 79)( 19, 78)( 20, 82)( 21, 81)( 22, 80)( 23, 89)( 24, 88)( 25, 92)
( 26, 91)( 27, 90)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 94)
( 34, 93)( 35, 97)( 36, 96)( 37, 95)( 38,104)( 39,103)( 40,107)( 41,106)
( 42,105)( 43, 99)( 44, 98)( 45,102)( 46,101)( 47,100)( 48,109)( 49,108)
( 50,112)( 51,111)( 52,110)( 53,119)( 54,118)( 55,122)( 56,121)( 57,120)
( 58,114)( 59,113)( 60,117)( 61,116)( 62,115)(123,199)(124,198)(125,202)
(126,201)(127,200)(128,209)(129,208)(130,212)(131,211)(132,210)(133,204)
(134,203)(135,207)(136,206)(137,205)(138,184)(139,183)(140,187)(141,186)
(142,185)(143,194)(144,193)(145,197)(146,196)(147,195)(148,189)(149,188)
(150,192)(151,191)(152,190)(153,229)(154,228)(155,232)(156,231)(157,230)
(158,239)(159,238)(160,242)(161,241)(162,240)(163,234)(164,233)(165,237)
(166,236)(167,235)(168,214)(169,213)(170,217)(171,216)(172,215)(173,224)
(174,223)(175,227)(176,226)(177,225)(178,219)(179,218)(180,222)(181,221)
(182,220);
s4 := Sym(242)!( 3, 8)( 4, 9)( 5, 10)( 6, 11)( 7, 12)( 18, 23)( 19, 24)
( 20, 25)( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)
( 48, 53)( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 98)( 64, 99)( 65,100)
( 66,101)( 67,102)( 68, 93)( 69, 94)( 70, 95)( 71, 96)( 72, 97)( 73,103)
( 74,104)( 75,105)( 76,106)( 77,107)( 78,113)( 79,114)( 80,115)( 81,116)
( 82,117)( 83,108)( 84,109)( 85,110)( 86,111)( 87,112)( 88,118)( 89,119)
( 90,120)( 91,121)( 92,122)(123,128)(124,129)(125,130)(126,131)(127,132)
(138,143)(139,144)(140,145)(141,146)(142,147)(153,158)(154,159)(155,160)
(156,161)(157,162)(168,173)(169,174)(170,175)(171,176)(172,177)(183,218)
(184,219)(185,220)(186,221)(187,222)(188,213)(189,214)(190,215)(191,216)
(192,217)(193,223)(194,224)(195,225)(196,226)(197,227)(198,233)(199,234)
(200,235)(201,236)(202,237)(203,228)(204,229)(205,230)(206,231)(207,232)
(208,238)(209,239)(210,240)(211,241)(212,242);
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope