Polytope of Type {2,30,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,14}*1680
if this polytope has a name.
Group : SmallGroup(1680,988)
Rank : 4
Schlafli Type : {2,30,14}
Number of vertices, edges, etc : 2, 30, 210, 14
Order of s₀s₁s₂s₃ : 210
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) :
   3-fold quotients : {2,10,14}*560
   5-fold quotients : {2,6,14}*336
   7-fold quotients : {2,30,2}*240
   14-fold quotients : {2,15,2}*120
   15-fold quotients : {2,2,14}*112
   21-fold quotients : {2,10,2}*80
   30-fold quotients : {2,2,7}*56
   35-fold quotients : {2,6,2}*48
   42-fold quotients : {2,5,2}*40
   70-fold quotients : {2,3,2}*24
   105-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope