Polytope of Type {10,35}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,35}*700
if this polytope has a name.
Group : SmallGroup(700,29)
Rank : 3
Schlafli Type : {10,35}
Number of vertices, edges, etc : 10, 175, 35
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 :
   {10,35,2} of size 1400
Vertex Figure Of :
   {2,10,35} of size 1400
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,35}*140
   7-fold quotients : {10,5}*100
   25-fold quotients : {2,7}*28
   35-fold quotients : {2,5}*20
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,70}*1400c
Irregular Quotients (of which this is a minimal cover):
   None.

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);;
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, s0*s1*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, 
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(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);
s1 := Sym(175)!(  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(175)!(  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);
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, s0*s1*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, 
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 >;
References : None.
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