Polytope of Type {30,6,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,6,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,240174)
Rank : 4
Schlafli Type : {30,6,2}
Number of vertices, edges, etc : 80, 240, 16, 2
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 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 : {30,6,2}*960
4-fold quotients : {15,6,2}*480
5-fold quotients : {6,6,2}*384b
10-fold quotients : {6,6,2}*192
20-fold quotients : {3,6,2}*96, {6,3,2}*96
24-fold quotients : {10,2,2}*80
40-fold quotients : {3,3,2}*48
48-fold quotients : {5,2,2}*40
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,121)( 2,122)( 3,126)( 4,125)( 5,124)( 6,123)( 7,128)( 8,127)( 9,153)( 10,154)( 11,158)( 12,157)( 13,156)( 14,155)( 15,160)( 16,159)( 17,145)( 18,146)( 19,150)( 20,149)( 21,148)( 22,147)( 23,152)( 24,151)( 25,137)( 26,138)( 27,142)( 28,141)( 29,140)( 30,139)( 31,144)( 32,143)( 33,129)( 34,130)( 35,134)( 36,133)( 37,132)( 38,131)( 39,136)( 40,135)( 41,201)( 42,202)( 43,206)( 44,205)( 45,204)( 46,203)( 47,208)( 48,207)( 49,233)( 50,234)( 51,238)( 52,237)( 53,236)( 54,235)( 55,240)( 56,239)( 57,225)( 58,226)( 59,230)( 60,229)( 61,228)( 62,227)( 63,232)( 64,231)( 65,217)( 66,218)( 67,222)( 68,221)( 69,220)( 70,219)( 71,224)( 72,223)( 73,209)( 74,210)( 75,214)( 76,213)( 77,212)( 78,211)( 79,216)( 80,215)( 81,161)( 82,162)( 83,166)( 84,165)( 85,164)( 86,163)( 87,168)( 88,167)( 89,193)( 90,194)( 91,198)( 92,197)( 93,196)( 94,195)( 95,200)( 96,199)( 97,185)( 98,186)( 99,190)(100,189)(101,188)(102,187)(103,192)(104,191)(105,177)(106,178)(107,182)(108,181)(109,180)(110,179)(111,184)(112,183)(113,169)(114,170)(115,174)(116,173)(117,172)(118,171)(119,176)(120,175);;
s1 := ( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 55)( 6, 56)( 7, 53)( 8, 54)( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)( 16, 46)( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 79)( 22, 80)( 23, 77)( 24, 78)( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 71)( 30, 72)( 31, 69)( 32, 70)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)( 40, 62)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97,113)( 98,114)( 99,116)(100,115)(101,119)(102,120)(103,117)(104,118)(107,108)(109,111)(110,112)(121,169)(122,170)(123,172)(124,171)(125,175)(126,176)(127,173)(128,174)(129,161)(130,162)(131,164)(132,163)(133,167)(134,168)(135,165)(136,166)(137,193)(138,194)(139,196)(140,195)(141,199)(142,200)(143,197)(144,198)(145,185)(146,186)(147,188)(148,187)(149,191)(150,192)(151,189)(152,190)(153,177)(154,178)(155,180)(156,179)(157,183)(158,184)(159,181)(160,182)(201,209)(202,210)(203,212)(204,211)(205,215)(206,216)(207,213)(208,214)(217,233)(218,234)(219,236)(220,235)(221,239)(222,240)(223,237)(224,238)(227,228)(229,231)(230,232);;
s2 := ( 1, 7)( 2, 8)( 5, 6)( 9, 15)( 10, 16)( 13, 14)( 17, 23)( 18, 24)( 21, 22)( 25, 31)( 26, 32)( 29, 30)( 33, 39)( 34, 40)( 37, 38)( 41, 87)( 42, 88)( 43, 83)( 44, 84)( 45, 86)( 46, 85)( 47, 81)( 48, 82)( 49, 95)( 50, 96)( 51, 91)( 52, 92)( 53, 94)( 54, 93)( 55, 89)( 56, 90)( 57,103)( 58,104)( 59, 99)( 60,100)( 61,102)( 62,101)( 63, 97)( 64, 98)( 65,111)( 66,112)( 67,107)( 68,108)( 69,110)( 70,109)( 71,105)( 72,106)( 73,119)( 74,120)( 75,115)( 76,116)( 77,118)( 78,117)( 79,113)( 80,114)(121,128)(122,127)(123,124)(129,136)(130,135)(131,132)(137,144)(138,143)(139,140)(145,152)(146,151)(147,148)(153,160)(154,159)(155,156)(161,208)(162,207)(163,204)(164,203)(165,205)(166,206)(167,202)(168,201)(169,216)(170,215)(171,212)(172,211)(173,213)(174,214)(175,210)(176,209)(177,224)(178,223)(179,220)(180,219)(181,221)(182,222)(183,218)(184,217)(185,232)(186,231)(187,228)(188,227)(189,229)(190,230)(191,226)(192,225)(193,240)(194,239)(195,236)(196,235)(197,237)(198,238)(199,234)(200,233);;
s3 := (241,242);;
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, s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(242)!( 1,121)( 2,122)( 3,126)( 4,125)( 5,124)( 6,123)( 7,128)( 8,127)( 9,153)( 10,154)( 11,158)( 12,157)( 13,156)( 14,155)( 15,160)( 16,159)( 17,145)( 18,146)( 19,150)( 20,149)( 21,148)( 22,147)( 23,152)( 24,151)( 25,137)( 26,138)( 27,142)( 28,141)( 29,140)( 30,139)( 31,144)( 32,143)( 33,129)( 34,130)( 35,134)( 36,133)( 37,132)( 38,131)( 39,136)( 40,135)( 41,201)( 42,202)( 43,206)( 44,205)( 45,204)( 46,203)( 47,208)( 48,207)( 49,233)( 50,234)( 51,238)( 52,237)( 53,236)( 54,235)( 55,240)( 56,239)( 57,225)( 58,226)( 59,230)( 60,229)( 61,228)( 62,227)( 63,232)( 64,231)( 65,217)( 66,218)( 67,222)( 68,221)( 69,220)( 70,219)( 71,224)( 72,223)( 73,209)( 74,210)( 75,214)( 76,213)( 77,212)( 78,211)( 79,216)( 80,215)( 81,161)( 82,162)( 83,166)( 84,165)( 85,164)( 86,163)( 87,168)( 88,167)( 89,193)( 90,194)( 91,198)( 92,197)( 93,196)( 94,195)( 95,200)( 96,199)( 97,185)( 98,186)( 99,190)(100,189)(101,188)(102,187)(103,192)(104,191)(105,177)(106,178)(107,182)(108,181)(109,180)(110,179)(111,184)(112,183)(113,169)(114,170)(115,174)(116,173)(117,172)(118,171)(119,176)(120,175);
s1 := Sym(242)!( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 55)( 6, 56)( 7, 53)( 8, 54)( 9, 41)( 10, 42)( 11, 44)( 12, 43)( 13, 47)( 14, 48)( 15, 45)( 16, 46)( 17, 73)( 18, 74)( 19, 76)( 20, 75)( 21, 79)( 22, 80)( 23, 77)( 24, 78)( 25, 65)( 26, 66)( 27, 68)( 28, 67)( 29, 71)( 30, 72)( 31, 69)( 32, 70)( 33, 57)( 34, 58)( 35, 60)( 36, 59)( 37, 63)( 38, 64)( 39, 61)( 40, 62)( 81, 89)( 82, 90)( 83, 92)( 84, 91)( 85, 95)( 86, 96)( 87, 93)( 88, 94)( 97,113)( 98,114)( 99,116)(100,115)(101,119)(102,120)(103,117)(104,118)(107,108)(109,111)(110,112)(121,169)(122,170)(123,172)(124,171)(125,175)(126,176)(127,173)(128,174)(129,161)(130,162)(131,164)(132,163)(133,167)(134,168)(135,165)(136,166)(137,193)(138,194)(139,196)(140,195)(141,199)(142,200)(143,197)(144,198)(145,185)(146,186)(147,188)(148,187)(149,191)(150,192)(151,189)(152,190)(153,177)(154,178)(155,180)(156,179)(157,183)(158,184)(159,181)(160,182)(201,209)(202,210)(203,212)(204,211)(205,215)(206,216)(207,213)(208,214)(217,233)(218,234)(219,236)(220,235)(221,239)(222,240)(223,237)(224,238)(227,228)(229,231)(230,232);
s2 := Sym(242)!( 1, 7)( 2, 8)( 5, 6)( 9, 15)( 10, 16)( 13, 14)( 17, 23)( 18, 24)( 21, 22)( 25, 31)( 26, 32)( 29, 30)( 33, 39)( 34, 40)( 37, 38)( 41, 87)( 42, 88)( 43, 83)( 44, 84)( 45, 86)( 46, 85)( 47, 81)( 48, 82)( 49, 95)( 50, 96)( 51, 91)( 52, 92)( 53, 94)( 54, 93)( 55, 89)( 56, 90)( 57,103)( 58,104)( 59, 99)( 60,100)( 61,102)( 62,101)( 63, 97)( 64, 98)( 65,111)( 66,112)( 67,107)( 68,108)( 69,110)( 70,109)( 71,105)( 72,106)( 73,119)( 74,120)( 75,115)( 76,116)( 77,118)( 78,117)( 79,113)( 80,114)(121,128)(122,127)(123,124)(129,136)(130,135)(131,132)(137,144)(138,143)(139,140)(145,152)(146,151)(147,148)(153,160)(154,159)(155,156)(161,208)(162,207)(163,204)(164,203)(165,205)(166,206)(167,202)(168,201)(169,216)(170,215)(171,212)(172,211)(173,213)(174,214)(175,210)(176,209)(177,224)(178,223)(179,220)(180,219)(181,221)(182,222)(183,218)(184,217)(185,232)(186,231)(187,228)(188,227)(189,229)(190,230)(191,226)(192,225)(193,240)(194,239)(195,236)(196,235)(197,237)(198,238)(199,234)(200,233);
s3 := Sym(242)!(241,242);
poly := sub<Sym(242)|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,
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >;
to this polytope