Polytope of Type {10,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,28}*1400
if this polytope has a name.
Group : SmallGroup(1400,129)
Rank : 3
Schlafli Type : {10,28}
Number of vertices, edges, etc : 25, 350, 70
Order of s₀s₁s₂ : 28
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {10,4}*200
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope