Polytope of Type {30,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,14}*840
Also Known As : {30,14|2}. if this polytope has another name.
Group : SmallGroup(840,171)
Rank : 3
Schlafli Type : {30,14}
Number of vertices, edges, etc : 30, 210, 14
Order of s₀s₁s₂ : 210
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {30,14,2} of size 1680
Vertex Figure Of :
   {2,30,14} of size 1680
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {10,14}*280
   5-fold quotients : {6,14}*168
   7-fold quotients : {30,2}*120
   14-fold quotients : {15,2}*60
   15-fold quotients : {2,14}*56
   21-fold quotients : {10,2}*40
   30-fold quotients : {2,7}*28
   35-fold quotients : {6,2}*24
   42-fold quotients : {5,2}*20
   70-fold quotients : {3,2}*12
   105-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,14}*1680, {30,28}*1680a
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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