Polytope of Type {176,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {176,2}*704
if this polytope has a name.
Group : SmallGroup(704,434)
Rank : 3
Schlafli Type : {176,2}
Number of vertices, edges, etc : 176, 176, 2
Order of s0s1s2 : 176
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{176,2,2} of size 1408
Vertex Figure Of :
{2,176,2} of size 1408
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {88,2}*352
4-fold quotients : {44,2}*176
8-fold quotients : {22,2}*88
11-fold quotients : {16,2}*64
16-fold quotients : {11,2}*44
22-fold quotients : {8,2}*32
44-fold quotients : {4,2}*16
88-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {176,4}*1408a, {352,2}*1408
Permutation Representation (GAP) :
s0 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)
( 16, 19)( 17, 18)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)
( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 45, 67)( 46, 77)( 47, 76)
( 48, 75)( 49, 74)( 50, 73)( 51, 72)( 52, 71)( 53, 70)( 54, 69)( 55, 68)
( 56, 78)( 57, 88)( 58, 87)( 59, 86)( 60, 85)( 61, 84)( 62, 83)( 63, 82)
( 64, 81)( 65, 80)( 66, 79)( 89,133)( 90,143)( 91,142)( 92,141)( 93,140)
( 94,139)( 95,138)( 96,137)( 97,136)( 98,135)( 99,134)(100,144)(101,154)
(102,153)(103,152)(104,151)(105,150)(106,149)(107,148)(108,147)(109,146)
(110,145)(111,166)(112,176)(113,175)(114,174)(115,173)(116,172)(117,171)
(118,170)(119,169)(120,168)(121,167)(122,155)(123,165)(124,164)(125,163)
(126,162)(127,161)(128,160)(129,159)(130,158)(131,157)(132,156);;
s1 := ( 1, 90)( 2, 89)( 3, 99)( 4, 98)( 5, 97)( 6, 96)( 7, 95)( 8, 94)
( 9, 93)( 10, 92)( 11, 91)( 12,101)( 13,100)( 14,110)( 15,109)( 16,108)
( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23,123)( 24,122)
( 25,132)( 26,131)( 27,130)( 28,129)( 29,128)( 30,127)( 31,126)( 32,125)
( 33,124)( 34,112)( 35,111)( 36,121)( 37,120)( 38,119)( 39,118)( 40,117)
( 41,116)( 42,115)( 43,114)( 44,113)( 45,156)( 46,155)( 47,165)( 48,164)
( 49,163)( 50,162)( 51,161)( 52,160)( 53,159)( 54,158)( 55,157)( 56,167)
( 57,166)( 58,176)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)( 64,170)
( 65,169)( 66,168)( 67,134)( 68,133)( 69,143)( 70,142)( 71,141)( 72,140)
( 73,139)( 74,138)( 75,137)( 76,136)( 77,135)( 78,145)( 79,144)( 80,154)
( 81,153)( 82,152)( 83,151)( 84,150)( 85,149)( 86,148)( 87,147)( 88,146);;
s2 := (177,178);;
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, s1*s2*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(178)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)
( 28, 40)( 29, 39)( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 45, 67)( 46, 77)
( 47, 76)( 48, 75)( 49, 74)( 50, 73)( 51, 72)( 52, 71)( 53, 70)( 54, 69)
( 55, 68)( 56, 78)( 57, 88)( 58, 87)( 59, 86)( 60, 85)( 61, 84)( 62, 83)
( 63, 82)( 64, 81)( 65, 80)( 66, 79)( 89,133)( 90,143)( 91,142)( 92,141)
( 93,140)( 94,139)( 95,138)( 96,137)( 97,136)( 98,135)( 99,134)(100,144)
(101,154)(102,153)(103,152)(104,151)(105,150)(106,149)(107,148)(108,147)
(109,146)(110,145)(111,166)(112,176)(113,175)(114,174)(115,173)(116,172)
(117,171)(118,170)(119,169)(120,168)(121,167)(122,155)(123,165)(124,164)
(125,163)(126,162)(127,161)(128,160)(129,159)(130,158)(131,157)(132,156);
s1 := Sym(178)!( 1, 90)( 2, 89)( 3, 99)( 4, 98)( 5, 97)( 6, 96)( 7, 95)
( 8, 94)( 9, 93)( 10, 92)( 11, 91)( 12,101)( 13,100)( 14,110)( 15,109)
( 16,108)( 17,107)( 18,106)( 19,105)( 20,104)( 21,103)( 22,102)( 23,123)
( 24,122)( 25,132)( 26,131)( 27,130)( 28,129)( 29,128)( 30,127)( 31,126)
( 32,125)( 33,124)( 34,112)( 35,111)( 36,121)( 37,120)( 38,119)( 39,118)
( 40,117)( 41,116)( 42,115)( 43,114)( 44,113)( 45,156)( 46,155)( 47,165)
( 48,164)( 49,163)( 50,162)( 51,161)( 52,160)( 53,159)( 54,158)( 55,157)
( 56,167)( 57,166)( 58,176)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)
( 64,170)( 65,169)( 66,168)( 67,134)( 68,133)( 69,143)( 70,142)( 71,141)
( 72,140)( 73,139)( 74,138)( 75,137)( 76,136)( 77,135)( 78,145)( 79,144)
( 80,154)( 81,153)( 82,152)( 83,151)( 84,150)( 85,149)( 86,148)( 87,147)
( 88,146);
s2 := Sym(178)!(177,178);
poly := sub<Sym(178)|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, s1*s2*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope