Polytope of Type {10,35,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,35,2}*1400
if this polytope has a name.
Group : SmallGroup(1400,146)
Rank : 4
Schlafli Type : {10,35,2}
Number of vertices, edges, etc : 10, 175, 35, 2
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 : {10,5,2}*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 := ( 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);;
s1 := (  1, 36)(  2, 42)(  3, 41)(  4, 40)(  5, 39)(  6, 38)(  7, 37)(  8, 64)
(  9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 57)( 16, 63)
( 17, 62)( 18, 61)( 19, 60)( 20, 59)( 21, 58)( 22, 50)( 23, 56)( 24, 55)
( 25, 54)( 26, 53)( 27, 52)( 28, 51)( 29, 43)( 30, 49)( 31, 48)( 32, 47)
( 33, 46)( 34, 45)( 35, 44)( 71,141)( 72,147)( 73,146)( 74,145)( 75,144)
( 76,143)( 77,142)( 78,169)( 79,175)( 80,174)( 81,173)( 82,172)( 83,171)
( 84,170)( 85,162)( 86,168)( 87,167)( 88,166)( 89,165)( 90,164)( 91,163)
( 92,155)( 93,161)( 94,160)( 95,159)( 96,158)( 97,157)( 98,156)( 99,148)
(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(107,112)(108,111)
(109,110)(113,134)(114,140)(115,139)(116,138)(117,137)(118,136)(119,135)
(120,127)(121,133)(122,132)(123,131)(124,130)(125,129)(126,128);;
s2 := (  1,  9)(  2,  8)(  3, 14)(  4, 13)(  5, 12)(  6, 11)(  7, 10)( 15, 30)
( 16, 29)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 31)( 22, 23)( 24, 28)
( 25, 27)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)( 41,151)( 42,150)
( 43,142)( 44,141)( 45,147)( 46,146)( 47,145)( 48,144)( 49,143)( 50,170)
( 51,169)( 52,175)( 53,174)( 54,173)( 55,172)( 56,171)( 57,163)( 58,162)
( 59,168)( 60,167)( 61,166)( 62,165)( 63,164)( 64,156)( 65,155)( 66,161)
( 67,160)( 68,159)( 69,158)( 70,157)( 71,114)( 72,113)( 73,119)( 74,118)
( 75,117)( 76,116)( 77,115)( 78,107)( 79,106)( 80,112)( 81,111)( 82,110)
( 83,109)( 84,108)( 85,135)( 86,134)( 87,140)( 88,139)( 89,138)( 90,137)
( 91,136)( 92,128)( 93,127)( 94,133)( 95,132)( 96,131)( 97,130)( 98,129)
( 99,121)(100,120)(101,126)(102,125)(103,124)(104,123)(105,122);;
s3 := (176,177);;
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, s2*s3*s2*s3, 
s2*s0*s1*s0*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, 
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)!( 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);
s1 := Sym(177)!(  1, 36)(  2, 42)(  3, 41)(  4, 40)(  5, 39)(  6, 38)(  7, 37)
(  8, 64)(  9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 57)
( 16, 63)( 17, 62)( 18, 61)( 19, 60)( 20, 59)( 21, 58)( 22, 50)( 23, 56)
( 24, 55)( 25, 54)( 26, 53)( 27, 52)( 28, 51)( 29, 43)( 30, 49)( 31, 48)
( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 71,141)( 72,147)( 73,146)( 74,145)
( 75,144)( 76,143)( 77,142)( 78,169)( 79,175)( 80,174)( 81,173)( 82,172)
( 83,171)( 84,170)( 85,162)( 86,168)( 87,167)( 88,166)( 89,165)( 90,164)
( 91,163)( 92,155)( 93,161)( 94,160)( 95,159)( 96,158)( 97,157)( 98,156)
( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(107,112)
(108,111)(109,110)(113,134)(114,140)(115,139)(116,138)(117,137)(118,136)
(119,135)(120,127)(121,133)(122,132)(123,131)(124,130)(125,129)(126,128);
s2 := Sym(177)!(  1,  9)(  2,  8)(  3, 14)(  4, 13)(  5, 12)(  6, 11)(  7, 10)
( 15, 30)( 16, 29)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 31)( 22, 23)
( 24, 28)( 25, 27)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)( 41,151)
( 42,150)( 43,142)( 44,141)( 45,147)( 46,146)( 47,145)( 48,144)( 49,143)
( 50,170)( 51,169)( 52,175)( 53,174)( 54,173)( 55,172)( 56,171)( 57,163)
( 58,162)( 59,168)( 60,167)( 61,166)( 62,165)( 63,164)( 64,156)( 65,155)
( 66,161)( 67,160)( 68,159)( 69,158)( 70,157)( 71,114)( 72,113)( 73,119)
( 74,118)( 75,117)( 76,116)( 77,115)( 78,107)( 79,106)( 80,112)( 81,111)
( 82,110)( 83,109)( 84,108)( 85,135)( 86,134)( 87,140)( 88,139)( 89,138)
( 90,137)( 91,136)( 92,128)( 93,127)( 94,133)( 95,132)( 96,131)( 97,130)
( 98,129)( 99,121)(100,120)(101,126)(102,125)(103,124)(104,123)(105,122);
s3 := Sym(177)!(176,177);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s2*s0*s1*s0*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, 
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