Polytope of Type {30,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4,4}*1920a
Also Known As : {{30,4|2},{4,4}4}. if this polytope has another name.
Group : SmallGroup(1920,151293)
Rank : 4
Schlafli Type : {30,4,4}
Number of vertices, edges, etc : 30, 120, 16, 8
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 : {30,4,4}*960
3-fold quotients : {10,4,4}*640
4-fold quotients : {30,2,4}*480, {30,4,2}*480a
5-fold quotients : {6,4,4}*384a
6-fold quotients : {10,4,4}*320
8-fold quotients : {15,2,4}*240, {30,2,2}*240
10-fold quotients : {6,4,4}*192
12-fold quotients : {10,2,4}*160, {10,4,2}*160
15-fold quotients : {2,4,4}*128
16-fold quotients : {15,2,2}*120
20-fold quotients : {6,2,4}*96, {6,4,2}*96a
24-fold quotients : {5,2,4}*80, {10,2,2}*80
30-fold quotients : {2,4,4}*64
40-fold quotients : {3,2,4}*48, {6,2,2}*48
48-fold quotients : {5,2,2}*40
60-fold quotients : {2,2,4}*32, {2,4,2}*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, 61)( 2, 65)( 3, 64)( 4, 63)( 5, 62)( 6, 71)( 7, 75)( 8, 74)
( 9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)( 16, 76)
( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 86)( 22, 90)( 23, 89)( 24, 88)
( 25, 87)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 91)( 32, 95)
( 33, 94)( 34, 93)( 35, 92)( 36,101)( 37,105)( 38,104)( 39,103)( 40,102)
( 41, 96)( 42,100)( 43, 99)( 44, 98)( 45, 97)( 46,106)( 47,110)( 48,109)
( 49,108)( 50,107)( 51,116)( 52,120)( 53,119)( 54,118)( 55,117)( 56,111)
( 57,115)( 58,114)( 59,113)( 60,112)(121,181)(122,185)(123,184)(124,183)
(125,182)(126,191)(127,195)(128,194)(129,193)(130,192)(131,186)(132,190)
(133,189)(134,188)(135,187)(136,196)(137,200)(138,199)(139,198)(140,197)
(141,206)(142,210)(143,209)(144,208)(145,207)(146,201)(147,205)(148,204)
(149,203)(150,202)(151,211)(152,215)(153,214)(154,213)(155,212)(156,221)
(157,225)(158,224)(159,223)(160,222)(161,216)(162,220)(163,219)(164,218)
(165,217)(166,226)(167,230)(168,229)(169,228)(170,227)(171,236)(172,240)
(173,239)(174,238)(175,237)(176,231)(177,235)(178,234)(179,233)(180,232);;
s1 := ( 1, 67)( 2, 66)( 3, 70)( 4, 69)( 5, 68)( 6, 62)( 7, 61)( 8, 65)
( 9, 64)( 10, 63)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)( 16, 82)
( 17, 81)( 18, 85)( 19, 84)( 20, 83)( 21, 77)( 22, 76)( 23, 80)( 24, 79)
( 25, 78)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31,112)( 32,111)
( 33,115)( 34,114)( 35,113)( 36,107)( 37,106)( 38,110)( 39,109)( 40,108)
( 41,117)( 42,116)( 43,120)( 44,119)( 45,118)( 46, 97)( 47, 96)( 48,100)
( 49, 99)( 50, 98)( 51, 92)( 52, 91)( 53, 95)( 54, 94)( 55, 93)( 56,102)
( 57,101)( 58,105)( 59,104)( 60,103)(121,187)(122,186)(123,190)(124,189)
(125,188)(126,182)(127,181)(128,185)(129,184)(130,183)(131,192)(132,191)
(133,195)(134,194)(135,193)(136,202)(137,201)(138,205)(139,204)(140,203)
(141,197)(142,196)(143,200)(144,199)(145,198)(146,207)(147,206)(148,210)
(149,209)(150,208)(151,232)(152,231)(153,235)(154,234)(155,233)(156,227)
(157,226)(158,230)(159,229)(160,228)(161,237)(162,236)(163,240)(164,239)
(165,238)(166,217)(167,216)(168,220)(169,219)(170,218)(171,212)(172,211)
(173,215)(174,214)(175,213)(176,222)(177,221)(178,225)(179,224)(180,223);;
s2 := (121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,157)(128,158)
(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)(135,165)(136,166)
(137,167)(138,168)(139,169)(140,170)(141,171)(142,172)(143,173)(144,174)
(145,175)(146,176)(147,177)(148,178)(149,179)(150,180)(181,211)(182,212)
(183,213)(184,214)(185,215)(186,216)(187,217)(188,218)(189,219)(190,220)
(191,221)(192,222)(193,223)(194,224)(195,225)(196,226)(197,227)(198,228)
(199,229)(200,230)(201,231)(202,232)(203,233)(204,234)(205,235)(206,236)
(207,237)(208,238)(209,239)(210,240);;
s3 := ( 1,121)( 2,122)( 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)( 63,183)( 64,184)
( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)
( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)
( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,208)
( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,216)
( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)(104,224)
(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)
(113,233)(114,234)(115,235)(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, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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, 61)( 2, 65)( 3, 64)( 4, 63)( 5, 62)( 6, 71)( 7, 75)
( 8, 74)( 9, 73)( 10, 72)( 11, 66)( 12, 70)( 13, 69)( 14, 68)( 15, 67)
( 16, 76)( 17, 80)( 18, 79)( 19, 78)( 20, 77)( 21, 86)( 22, 90)( 23, 89)
( 24, 88)( 25, 87)( 26, 81)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 91)
( 32, 95)( 33, 94)( 34, 93)( 35, 92)( 36,101)( 37,105)( 38,104)( 39,103)
( 40,102)( 41, 96)( 42,100)( 43, 99)( 44, 98)( 45, 97)( 46,106)( 47,110)
( 48,109)( 49,108)( 50,107)( 51,116)( 52,120)( 53,119)( 54,118)( 55,117)
( 56,111)( 57,115)( 58,114)( 59,113)( 60,112)(121,181)(122,185)(123,184)
(124,183)(125,182)(126,191)(127,195)(128,194)(129,193)(130,192)(131,186)
(132,190)(133,189)(134,188)(135,187)(136,196)(137,200)(138,199)(139,198)
(140,197)(141,206)(142,210)(143,209)(144,208)(145,207)(146,201)(147,205)
(148,204)(149,203)(150,202)(151,211)(152,215)(153,214)(154,213)(155,212)
(156,221)(157,225)(158,224)(159,223)(160,222)(161,216)(162,220)(163,219)
(164,218)(165,217)(166,226)(167,230)(168,229)(169,228)(170,227)(171,236)
(172,240)(173,239)(174,238)(175,237)(176,231)(177,235)(178,234)(179,233)
(180,232);
s1 := Sym(240)!( 1, 67)( 2, 66)( 3, 70)( 4, 69)( 5, 68)( 6, 62)( 7, 61)
( 8, 65)( 9, 64)( 10, 63)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)
( 16, 82)( 17, 81)( 18, 85)( 19, 84)( 20, 83)( 21, 77)( 22, 76)( 23, 80)
( 24, 79)( 25, 78)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31,112)
( 32,111)( 33,115)( 34,114)( 35,113)( 36,107)( 37,106)( 38,110)( 39,109)
( 40,108)( 41,117)( 42,116)( 43,120)( 44,119)( 45,118)( 46, 97)( 47, 96)
( 48,100)( 49, 99)( 50, 98)( 51, 92)( 52, 91)( 53, 95)( 54, 94)( 55, 93)
( 56,102)( 57,101)( 58,105)( 59,104)( 60,103)(121,187)(122,186)(123,190)
(124,189)(125,188)(126,182)(127,181)(128,185)(129,184)(130,183)(131,192)
(132,191)(133,195)(134,194)(135,193)(136,202)(137,201)(138,205)(139,204)
(140,203)(141,197)(142,196)(143,200)(144,199)(145,198)(146,207)(147,206)
(148,210)(149,209)(150,208)(151,232)(152,231)(153,235)(154,234)(155,233)
(156,227)(157,226)(158,230)(159,229)(160,228)(161,237)(162,236)(163,240)
(164,239)(165,238)(166,217)(167,216)(168,220)(169,219)(170,218)(171,212)
(172,211)(173,215)(174,214)(175,213)(176,222)(177,221)(178,225)(179,224)
(180,223);
s2 := Sym(240)!(121,151)(122,152)(123,153)(124,154)(125,155)(126,156)(127,157)
(128,158)(129,159)(130,160)(131,161)(132,162)(133,163)(134,164)(135,165)
(136,166)(137,167)(138,168)(139,169)(140,170)(141,171)(142,172)(143,173)
(144,174)(145,175)(146,176)(147,177)(148,178)(149,179)(150,180)(181,211)
(182,212)(183,213)(184,214)(185,215)(186,216)(187,217)(188,218)(189,219)
(190,220)(191,221)(192,222)(193,223)(194,224)(195,225)(196,226)(197,227)
(198,228)(199,229)(200,230)(201,231)(202,232)(203,233)(204,234)(205,235)
(206,236)(207,237)(208,238)(209,239)(210,240);
s3 := Sym(240)!( 1,121)( 2,122)( 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)( 63,183)
( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)
( 72,192)( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)
( 80,200)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)
( 88,208)( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)
( 96,216)( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)
(104,224)(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)
(112,232)(113,233)(114,234)(115,235)(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,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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