Polytope of Type {70,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {70,10}*1400a
if this polytope has a name.
Group : SmallGroup(1400,133)
Rank : 3
Schlafli Type : {70,10}
Number of vertices, edges, etc : 70, 350, 10
Order of s₀s₁s₂ : 70
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {14,10}*280
   7-fold quotients : {10,10}*200b
   14-fold quotients : {10,5}*100
   25-fold quotients : {14,2}*56
   35-fold quotients : {2,10}*40
   50-fold quotients : {7,2}*28
   70-fold quotients : {2,5}*20
   175-fold quotients : {2,2}*8
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)( 36,141)
( 37,147)( 38,146)( 39,145)( 40,144)( 41,143)( 42,142)( 43,148)( 44,154)
( 45,153)( 46,152)( 47,151)( 48,150)( 49,149)( 50,155)( 51,161)( 52,160)
( 53,159)( 54,158)( 55,157)( 56,156)( 57,162)( 58,168)( 59,167)( 60,166)
( 61,165)( 62,164)( 63,163)( 64,169)( 65,175)( 66,174)( 67,173)( 68,172)
( 69,171)( 70,170)( 71,106)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)
( 77,107)( 78,113)( 79,119)( 80,118)( 81,117)( 82,116)( 83,115)( 84,114)
( 85,120)( 86,126)( 87,125)( 88,124)( 89,123)( 90,122)( 91,121)( 92,127)
( 93,133)( 94,132)( 95,131)( 96,130)( 97,129)( 98,128)( 99,134)(100,140)
(101,139)(102,138)(103,137)(104,136)(105,135);;
s1 := (  1, 37)(  2, 36)(  3, 42)(  4, 41)(  5, 40)(  6, 39)(  7, 38)(  8, 65)
(  9, 64)( 10, 70)( 11, 69)( 12, 68)( 13, 67)( 14, 66)( 15, 58)( 16, 57)
( 17, 63)( 18, 62)( 19, 61)( 20, 60)( 21, 59)( 22, 51)( 23, 50)( 24, 56)
( 25, 55)( 26, 54)( 27, 53)( 28, 52)( 29, 44)( 30, 43)( 31, 49)( 32, 48)
( 33, 47)( 34, 46)( 35, 45)( 71,142)( 72,141)( 73,147)( 74,146)( 75,145)
( 76,144)( 77,143)( 78,170)( 79,169)( 80,175)( 81,174)( 82,173)( 83,172)
( 84,171)( 85,163)( 86,162)( 87,168)( 88,167)( 89,166)( 90,165)( 91,164)
( 92,156)( 93,155)( 94,161)( 95,160)( 96,159)( 97,158)( 98,157)( 99,149)
(100,148)(101,154)(102,153)(103,152)(104,151)(105,150)(106,107)(108,112)
(109,111)(113,135)(114,134)(115,140)(116,139)(117,138)(118,137)(119,136)
(120,128)(121,127)(122,133)(123,132)(124,131)(125,130)(126,129);;
s2 := (  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]);;

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

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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope