Polytope of Type {2,14,30}

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

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