Polytope of Type {28,10}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope