Polytope of Type {2,16,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,16,30}*1920
if this polytope has a name.
Group : SmallGroup(1920,203894)
Rank : 4
Schlafli Type : {2,16,30}
Number of vertices, edges, etc : 2, 16, 240, 30
Order of s₀s₁s₂s₃ : 240
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 : {2,8,30}*960
   3-fold quotients : {2,16,10}*640
   4-fold quotients : {2,4,30}*480a
   5-fold quotients : {2,16,6}*384
   6-fold quotients : {2,8,10}*320
   8-fold quotients : {2,2,30}*240
   10-fold quotients : {2,8,6}*192
   12-fold quotients : {2,4,10}*160
   15-fold quotients : {2,16,2}*128
   16-fold quotients : {2,2,15}*120
   20-fold quotients : {2,4,6}*96a
   24-fold quotients : {2,2,10}*80
   30-fold quotients : {2,8,2}*64
   40-fold quotients : {2,2,6}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,4,2}*32
   80-fold quotients : {2,2,3}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope