Polytope of Type {2,35,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,35,10}*1400
if this polytope has a name.
Group : SmallGroup(1400,146)
Rank : 4
Schlafli Type : {2,35,10}
Number of vertices, edges, etc : 2, 35, 175, 10
Order of s₀s₁s₂s₃ : 70
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) :
   5-fold quotients : {2,35,2}*280
   7-fold quotients : {2,5,10}*200
   25-fold quotients : {2,7,2}*56
   35-fold quotients : {2,5,2}*40
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope