Polytope of Type {14,10,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,10,5}*1400
if this polytope has a name.
Group : SmallGroup(1400,133)
Rank : 4
Schlafli Type : {14,10,5}
Number of vertices, edges, etc : 14, 70, 25, 5
Order of s₀s₁s₂s₃ : 70
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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) :
   5-fold quotients : {14,2,5}*280
   7-fold quotients : {2,10,5}*200
   10-fold quotients : {7,2,5}*140
   35-fold quotients : {2,2,5}*40
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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