Polytope of Type {35,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {35,10}*700
if this polytope has a name.
Group : SmallGroup(700,29)
Rank : 3
Schlafli Type : {35,10}
Number of vertices, edges, etc : 35, 175, 10
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 :
   {35,10,2} of size 1400
Vertex Figure Of :
   {2,35,10} of size 1400
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {35,2}*140
   7-fold quotients : {5,10}*100
   25-fold quotients : {7,2}*28
   35-fold quotients : {5,2}*20
Covers (Minimal Covers in Boldface) :
   2-fold covers : {70,10}*1400c
Permutation Representation (GAP) :

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