Polytope of Type {10,70}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,70}*1400a
if this polytope has a name.
Group : SmallGroup(1400,133)
Rank : 3
Schlafli Type : {10,70}
Number of vertices, edges, etc : 10, 350, 70
Order of s₀s₁s₂ : 70
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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 : {10,14}*280
   7-fold quotients : {10,10}*200c
   14-fold quotients : {5,10}*100
   25-fold quotients : {2,14}*56
   35-fold quotients : {10,2}*40
   50-fold quotients : {2,7}*28
   70-fold quotients : {5,2}*20
   175-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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)( 36,141)( 37,142)
( 38,143)( 39,144)( 40,145)( 41,146)( 42,147)( 43,169)( 44,170)( 45,171)
( 46,172)( 47,173)( 48,174)( 49,175)( 50,162)( 51,163)( 52,164)( 53,165)
( 54,166)( 55,167)( 56,168)( 57,155)( 58,156)( 59,157)( 60,158)( 61,159)
( 62,160)( 63,161)( 64,148)( 65,149)( 66,150)( 67,151)( 68,152)( 69,153)
( 70,154)( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)
( 78,134)( 79,135)( 80,136)( 81,137)( 82,138)( 83,139)( 84,140)( 85,127)
( 86,128)( 87,129)( 88,130)( 89,131)( 90,132)( 91,133)( 92,120)( 93,121)
( 94,122)( 95,123)( 96,124)( 97,125)( 98,126)( 99,113)(100,114)(101,115)
(102,116)(103,117)(104,118)(105,119);;
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)( 71,148)( 72,154)( 73,153)( 74,152)( 75,151)
( 76,150)( 77,149)( 78,141)( 79,147)( 80,146)( 81,145)( 82,144)( 83,143)
( 84,142)( 85,169)( 86,175)( 87,174)( 88,173)( 89,172)( 90,171)( 91,170)
( 92,162)( 93,168)( 94,167)( 95,166)( 96,165)( 97,164)( 98,163)( 99,155)
(100,161)(101,160)(102,159)(103,158)(104,157)(105,156)(106,113)(107,119)
(108,118)(109,117)(110,116)(111,115)(112,114)(120,134)(121,140)(122,139)
(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)(130,131);;
s2 := (  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);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*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*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(175)!(  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)( 36,141)
( 37,142)( 38,143)( 39,144)( 40,145)( 41,146)( 42,147)( 43,169)( 44,170)
( 45,171)( 46,172)( 47,173)( 48,174)( 49,175)( 50,162)( 51,163)( 52,164)
( 53,165)( 54,166)( 55,167)( 56,168)( 57,155)( 58,156)( 59,157)( 60,158)
( 61,159)( 62,160)( 63,161)( 64,148)( 65,149)( 66,150)( 67,151)( 68,152)
( 69,153)( 70,154)( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)
( 77,112)( 78,134)( 79,135)( 80,136)( 81,137)( 82,138)( 83,139)( 84,140)
( 85,127)( 86,128)( 87,129)( 88,130)( 89,131)( 90,132)( 91,133)( 92,120)
( 93,121)( 94,122)( 95,123)( 96,124)( 97,125)( 98,126)( 99,113)(100,114)
(101,115)(102,116)(103,117)(104,118)(105,119);
s1 := Sym(175)!(  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)( 71,148)( 72,154)( 73,153)( 74,152)
( 75,151)( 76,150)( 77,149)( 78,141)( 79,147)( 80,146)( 81,145)( 82,144)
( 83,143)( 84,142)( 85,169)( 86,175)( 87,174)( 88,173)( 89,172)( 90,171)
( 91,170)( 92,162)( 93,168)( 94,167)( 95,166)( 96,165)( 97,164)( 98,163)
( 99,155)(100,161)(101,160)(102,159)(103,158)(104,157)(105,156)(106,113)
(107,119)(108,118)(109,117)(110,116)(111,115)(112,114)(120,134)(121,140)
(122,139)(123,138)(124,137)(125,136)(126,135)(128,133)(129,132)(130,131);
s2 := 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);
poly := sub<Sym(175)|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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*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*s2*s1 >;

References : None.
to this polytope