Polytope of Type {2,22,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,16}*1408
if this polytope has a name.
Group : SmallGroup(1408,17614)
Rank : 4
Schlafli Type : {2,22,16}
Number of vertices, edges, etc : 2, 22, 176, 16
Order of s₀s₁s₂s₃ : 176
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,22,8}*704
   4-fold quotients : {2,22,4}*352
   8-fold quotients : {2,22,2}*176
   11-fold quotients : {2,2,16}*128
   16-fold quotients : {2,11,2}*88
   22-fold quotients : {2,2,8}*64
   44-fold quotients : {2,2,4}*32
   88-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)( 17, 22)
( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)( 37, 46)
( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)( 51, 54)
( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 70, 79)( 71, 78)
( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)( 85, 86)
( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(103,112)(104,111)(105,110)
(106,109)(107,108)(114,123)(115,122)(116,121)(117,120)(118,119)(125,134)
(126,133)(127,132)(128,131)(129,130)(136,145)(137,144)(138,143)(139,142)
(140,141)(147,156)(148,155)(149,154)(150,153)(151,152)(158,167)(159,166)
(160,165)(161,164)(162,163)(169,178)(170,177)(171,176)(172,175)(173,174);;
s2 := (  3,  4)(  5, 13)(  6, 12)(  7, 11)(  8, 10)( 14, 15)( 16, 24)( 17, 23)
( 18, 22)( 19, 21)( 25, 37)( 26, 36)( 27, 46)( 28, 45)( 29, 44)( 30, 43)
( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 47, 70)( 48, 69)( 49, 79)
( 50, 78)( 51, 77)( 52, 76)( 53, 75)( 54, 74)( 55, 73)( 56, 72)( 57, 71)
( 58, 81)( 59, 80)( 60, 90)( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 85)
( 66, 84)( 67, 83)( 68, 82)( 91,136)( 92,135)( 93,145)( 94,144)( 95,143)
( 96,142)( 97,141)( 98,140)( 99,139)(100,138)(101,137)(102,147)(103,146)
(104,156)(105,155)(106,154)(107,153)(108,152)(109,151)(110,150)(111,149)
(112,148)(113,169)(114,168)(115,178)(116,177)(117,176)(118,175)(119,174)
(120,173)(121,172)(122,171)(123,170)(124,158)(125,157)(126,167)(127,166)
(128,165)(129,164)(130,163)(131,162)(132,161)(133,160)(134,159);;
s3 := (  3, 91)(  4, 92)(  5, 93)(  6, 94)(  7, 95)(  8, 96)(  9, 97)( 10, 98)
( 11, 99)( 12,100)( 13,101)( 14,102)( 15,103)( 16,104)( 17,105)( 18,106)
( 19,107)( 20,108)( 21,109)( 22,110)( 23,111)( 24,112)( 25,124)( 26,125)
( 27,126)( 28,127)( 29,128)( 30,129)( 31,130)( 32,131)( 33,132)( 34,133)
( 35,134)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)( 41,118)( 42,119)
( 43,120)( 44,121)( 45,122)( 46,123)( 47,157)( 48,158)( 49,159)( 50,160)
( 51,161)( 52,162)( 53,163)( 54,164)( 55,165)( 56,166)( 57,167)( 58,168)
( 59,169)( 60,170)( 61,171)( 62,172)( 63,173)( 64,174)( 65,175)( 66,176)
( 67,177)( 68,178)( 69,135)( 70,136)( 71,137)( 72,138)( 73,139)( 74,140)
( 75,141)( 76,142)( 77,143)( 78,144)( 79,145)( 80,146)( 81,147)( 82,148)
( 83,149)( 84,150)( 85,151)( 86,152)( 87,153)( 88,154)( 89,155)( 90,156);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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(178)!(1,2);
s1 := Sym(178)!(  4, 13)(  5, 12)(  6, 11)(  7, 10)(  8,  9)( 15, 24)( 16, 23)
( 17, 22)( 18, 21)( 19, 20)( 26, 35)( 27, 34)( 28, 33)( 29, 32)( 30, 31)
( 37, 46)( 38, 45)( 39, 44)( 40, 43)( 41, 42)( 48, 57)( 49, 56)( 50, 55)
( 51, 54)( 52, 53)( 59, 68)( 60, 67)( 61, 66)( 62, 65)( 63, 64)( 70, 79)
( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 81, 90)( 82, 89)( 83, 88)( 84, 87)
( 85, 86)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(103,112)(104,111)
(105,110)(106,109)(107,108)(114,123)(115,122)(116,121)(117,120)(118,119)
(125,134)(126,133)(127,132)(128,131)(129,130)(136,145)(137,144)(138,143)
(139,142)(140,141)(147,156)(148,155)(149,154)(150,153)(151,152)(158,167)
(159,166)(160,165)(161,164)(162,163)(169,178)(170,177)(171,176)(172,175)
(173,174);
s2 := Sym(178)!(  3,  4)(  5, 13)(  6, 12)(  7, 11)(  8, 10)( 14, 15)( 16, 24)
( 17, 23)( 18, 22)( 19, 21)( 25, 37)( 26, 36)( 27, 46)( 28, 45)( 29, 44)
( 30, 43)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 47, 70)( 48, 69)
( 49, 79)( 50, 78)( 51, 77)( 52, 76)( 53, 75)( 54, 74)( 55, 73)( 56, 72)
( 57, 71)( 58, 81)( 59, 80)( 60, 90)( 61, 89)( 62, 88)( 63, 87)( 64, 86)
( 65, 85)( 66, 84)( 67, 83)( 68, 82)( 91,136)( 92,135)( 93,145)( 94,144)
( 95,143)( 96,142)( 97,141)( 98,140)( 99,139)(100,138)(101,137)(102,147)
(103,146)(104,156)(105,155)(106,154)(107,153)(108,152)(109,151)(110,150)
(111,149)(112,148)(113,169)(114,168)(115,178)(116,177)(117,176)(118,175)
(119,174)(120,173)(121,172)(122,171)(123,170)(124,158)(125,157)(126,167)
(127,166)(128,165)(129,164)(130,163)(131,162)(132,161)(133,160)(134,159);
s3 := Sym(178)!(  3, 91)(  4, 92)(  5, 93)(  6, 94)(  7, 95)(  8, 96)(  9, 97)
( 10, 98)( 11, 99)( 12,100)( 13,101)( 14,102)( 15,103)( 16,104)( 17,105)
( 18,106)( 19,107)( 20,108)( 21,109)( 22,110)( 23,111)( 24,112)( 25,124)
( 26,125)( 27,126)( 28,127)( 29,128)( 30,129)( 31,130)( 32,131)( 33,132)
( 34,133)( 35,134)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)( 41,118)
( 42,119)( 43,120)( 44,121)( 45,122)( 46,123)( 47,157)( 48,158)( 49,159)
( 50,160)( 51,161)( 52,162)( 53,163)( 54,164)( 55,165)( 56,166)( 57,167)
( 58,168)( 59,169)( 60,170)( 61,171)( 62,172)( 63,173)( 64,174)( 65,175)
( 66,176)( 67,177)( 68,178)( 69,135)( 70,136)( 71,137)( 72,138)( 73,139)
( 74,140)( 75,141)( 76,142)( 77,143)( 78,144)( 79,145)( 80,146)( 81,147)
( 82,148)( 83,149)( 84,150)( 85,151)( 86,152)( 87,153)( 88,154)( 89,155)
( 90,156);
poly := sub<Sym(178)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >;

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