Polytope of Type {2,6,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,30}*1920
if this polytope has a name.
Group : SmallGroup(1920,240174)
Rank : 4
Schlafli Type : {2,6,30}
Number of vertices, edges, etc : 2, 16, 240, 80
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 : {2,6,30}*960
   4-fold quotients : {2,6,15}*480
   5-fold quotients : {2,6,6}*384b
   10-fold quotients : {2,6,6}*192
   20-fold quotients : {2,3,6}*96, {2,6,3}*96
   24-fold quotients : {2,2,10}*80
   40-fold quotients : {2,3,3}*48
   48-fold quotients : {2,2,5}*40
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  5,  8)(  6,  7)(  9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)( 22, 23)
( 25, 26)( 29, 32)( 30, 31)( 33, 34)( 37, 40)( 38, 39)( 41, 42)( 43, 83)
( 44, 84)( 45, 88)( 46, 87)( 47, 86)( 48, 85)( 49, 90)( 50, 89)( 51, 91)
( 52, 92)( 53, 96)( 54, 95)( 55, 94)( 56, 93)( 57, 98)( 58, 97)( 59, 99)
( 60,100)( 61,104)( 62,103)( 63,102)( 64,101)( 65,106)( 66,105)( 67,107)
( 68,108)( 69,112)( 70,111)( 71,110)( 72,109)( 73,114)( 74,113)( 75,115)
( 76,116)( 77,120)( 78,119)( 79,118)( 80,117)( 81,122)( 82,121)(123,124)
(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)(142,144)
(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(163,204)(164,203)
(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)(171,212)(172,211)
(173,215)(174,216)(175,213)(176,214)(177,217)(178,218)(179,220)(180,219)
(181,223)(182,224)(183,221)(184,222)(185,225)(186,226)(187,228)(188,227)
(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)(195,236)(196,235)
(197,239)(198,240)(199,237)(200,238)(201,241)(202,242);;
s2 := (  3, 43)(  4, 44)(  5, 46)(  6, 45)(  7, 49)(  8, 50)(  9, 47)( 10, 48)
( 11, 75)( 12, 76)( 13, 78)( 14, 77)( 15, 81)( 16, 82)( 17, 79)( 18, 80)
( 19, 67)( 20, 68)( 21, 70)( 22, 69)( 23, 73)( 24, 74)( 25, 71)( 26, 72)
( 27, 59)( 28, 60)( 29, 62)( 30, 61)( 31, 65)( 32, 66)( 33, 63)( 34, 64)
( 35, 51)( 36, 52)( 37, 54)( 38, 53)( 39, 57)( 40, 58)( 41, 55)( 42, 56)
( 85, 86)( 87, 89)( 88, 90)( 91,115)( 92,116)( 93,118)( 94,117)( 95,121)
( 96,122)( 97,119)( 98,120)( 99,107)(100,108)(101,110)(102,109)(103,113)
(104,114)(105,111)(106,112)(123,163)(124,164)(125,166)(126,165)(127,169)
(128,170)(129,167)(130,168)(131,195)(132,196)(133,198)(134,197)(135,201)
(136,202)(137,199)(138,200)(139,187)(140,188)(141,190)(142,189)(143,193)
(144,194)(145,191)(146,192)(147,179)(148,180)(149,182)(150,181)(151,185)
(152,186)(153,183)(154,184)(155,171)(156,172)(157,174)(158,173)(159,177)
(160,178)(161,175)(162,176)(205,206)(207,209)(208,210)(211,235)(212,236)
(213,238)(214,237)(215,241)(216,242)(217,239)(218,240)(219,227)(220,228)
(221,230)(222,229)(223,233)(224,234)(225,231)(226,232);;
s3 := (  3,137)(  4,138)(  5,133)(  6,134)(  7,136)(  8,135)(  9,131)( 10,132)
( 11,129)( 12,130)( 13,125)( 14,126)( 15,128)( 16,127)( 17,123)( 18,124)
( 19,161)( 20,162)( 21,157)( 22,158)( 23,160)( 24,159)( 25,155)( 26,156)
( 27,153)( 28,154)( 29,149)( 30,150)( 31,152)( 32,151)( 33,147)( 34,148)
( 35,145)( 36,146)( 37,141)( 38,142)( 39,144)( 40,143)( 41,139)( 42,140)
( 43,217)( 44,218)( 45,213)( 46,214)( 47,216)( 48,215)( 49,211)( 50,212)
( 51,209)( 52,210)( 53,205)( 54,206)( 55,208)( 56,207)( 57,203)( 58,204)
( 59,241)( 60,242)( 61,237)( 62,238)( 63,240)( 64,239)( 65,235)( 66,236)
( 67,233)( 68,234)( 69,229)( 70,230)( 71,232)( 72,231)( 73,227)( 74,228)
( 75,225)( 76,226)( 77,221)( 78,222)( 79,224)( 80,223)( 81,219)( 82,220)
( 83,177)( 84,178)( 85,173)( 86,174)( 87,176)( 88,175)( 89,171)( 90,172)
( 91,169)( 92,170)( 93,165)( 94,166)( 95,168)( 96,167)( 97,163)( 98,164)
( 99,201)(100,202)(101,197)(102,198)(103,200)(104,199)(105,195)(106,196)
(107,193)(108,194)(109,189)(110,190)(111,192)(112,191)(113,187)(114,188)
(115,185)(116,186)(117,181)(118,182)(119,184)(120,183)(121,179)(122,180);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s3*s2*s1*s2, 
s3*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s2*s3*s2*s1*s3*s2*s1*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(242)!(1,2);
s1 := Sym(242)!(  5,  8)(  6,  7)(  9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)
( 22, 23)( 25, 26)( 29, 32)( 30, 31)( 33, 34)( 37, 40)( 38, 39)( 41, 42)
( 43, 83)( 44, 84)( 45, 88)( 46, 87)( 47, 86)( 48, 85)( 49, 90)( 50, 89)
( 51, 91)( 52, 92)( 53, 96)( 54, 95)( 55, 94)( 56, 93)( 57, 98)( 58, 97)
( 59, 99)( 60,100)( 61,104)( 62,103)( 63,102)( 64,101)( 65,106)( 66,105)
( 67,107)( 68,108)( 69,112)( 70,111)( 71,110)( 72,109)( 73,114)( 74,113)
( 75,115)( 76,116)( 77,120)( 78,119)( 79,118)( 80,117)( 81,122)( 82,121)
(123,124)(125,127)(126,128)(131,132)(133,135)(134,136)(139,140)(141,143)
(142,144)(147,148)(149,151)(150,152)(155,156)(157,159)(158,160)(163,204)
(164,203)(165,207)(166,208)(167,205)(168,206)(169,209)(170,210)(171,212)
(172,211)(173,215)(174,216)(175,213)(176,214)(177,217)(178,218)(179,220)
(180,219)(181,223)(182,224)(183,221)(184,222)(185,225)(186,226)(187,228)
(188,227)(189,231)(190,232)(191,229)(192,230)(193,233)(194,234)(195,236)
(196,235)(197,239)(198,240)(199,237)(200,238)(201,241)(202,242);
s2 := Sym(242)!(  3, 43)(  4, 44)(  5, 46)(  6, 45)(  7, 49)(  8, 50)(  9, 47)
( 10, 48)( 11, 75)( 12, 76)( 13, 78)( 14, 77)( 15, 81)( 16, 82)( 17, 79)
( 18, 80)( 19, 67)( 20, 68)( 21, 70)( 22, 69)( 23, 73)( 24, 74)( 25, 71)
( 26, 72)( 27, 59)( 28, 60)( 29, 62)( 30, 61)( 31, 65)( 32, 66)( 33, 63)
( 34, 64)( 35, 51)( 36, 52)( 37, 54)( 38, 53)( 39, 57)( 40, 58)( 41, 55)
( 42, 56)( 85, 86)( 87, 89)( 88, 90)( 91,115)( 92,116)( 93,118)( 94,117)
( 95,121)( 96,122)( 97,119)( 98,120)( 99,107)(100,108)(101,110)(102,109)
(103,113)(104,114)(105,111)(106,112)(123,163)(124,164)(125,166)(126,165)
(127,169)(128,170)(129,167)(130,168)(131,195)(132,196)(133,198)(134,197)
(135,201)(136,202)(137,199)(138,200)(139,187)(140,188)(141,190)(142,189)
(143,193)(144,194)(145,191)(146,192)(147,179)(148,180)(149,182)(150,181)
(151,185)(152,186)(153,183)(154,184)(155,171)(156,172)(157,174)(158,173)
(159,177)(160,178)(161,175)(162,176)(205,206)(207,209)(208,210)(211,235)
(212,236)(213,238)(214,237)(215,241)(216,242)(217,239)(218,240)(219,227)
(220,228)(221,230)(222,229)(223,233)(224,234)(225,231)(226,232);
s3 := Sym(242)!(  3,137)(  4,138)(  5,133)(  6,134)(  7,136)(  8,135)(  9,131)
( 10,132)( 11,129)( 12,130)( 13,125)( 14,126)( 15,128)( 16,127)( 17,123)
( 18,124)( 19,161)( 20,162)( 21,157)( 22,158)( 23,160)( 24,159)( 25,155)
( 26,156)( 27,153)( 28,154)( 29,149)( 30,150)( 31,152)( 32,151)( 33,147)
( 34,148)( 35,145)( 36,146)( 37,141)( 38,142)( 39,144)( 40,143)( 41,139)
( 42,140)( 43,217)( 44,218)( 45,213)( 46,214)( 47,216)( 48,215)( 49,211)
( 50,212)( 51,209)( 52,210)( 53,205)( 54,206)( 55,208)( 56,207)( 57,203)
( 58,204)( 59,241)( 60,242)( 61,237)( 62,238)( 63,240)( 64,239)( 65,235)
( 66,236)( 67,233)( 68,234)( 69,229)( 70,230)( 71,232)( 72,231)( 73,227)
( 74,228)( 75,225)( 76,226)( 77,221)( 78,222)( 79,224)( 80,223)( 81,219)
( 82,220)( 83,177)( 84,178)( 85,173)( 86,174)( 87,176)( 88,175)( 89,171)
( 90,172)( 91,169)( 92,170)( 93,165)( 94,166)( 95,168)( 96,167)( 97,163)
( 98,164)( 99,201)(100,202)(101,197)(102,198)(103,200)(104,199)(105,195)
(106,196)(107,193)(108,194)(109,189)(110,190)(111,192)(112,191)(113,187)
(114,188)(115,185)(116,186)(117,181)(118,182)(119,184)(120,183)(121,179)
(122,180);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s3*s2*s1*s2, 
s3*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s2*s3*s2*s1*s3*s2*s1*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3 >;

to this polytope