Polytope of Type {22,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,16}*704
Also Known As : {22,16|2}. if this polytope has another name.
Group : SmallGroup(704,442)
Rank : 3
Schlafli Type : {22,16}
Number of vertices, edges, etc : 22, 176, 16
Order of s₀s₁s₂ : 176
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {22,16,2} of size 1408
Vertex Figure Of :
   {2,22,16} of size 1408
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {22,8}*352
   4-fold quotients : {22,4}*176
   8-fold quotients : {22,2}*88
   11-fold quotients : {2,16}*64
   16-fold quotients : {11,2}*44
   22-fold quotients : {2,8}*32
   44-fold quotients : {2,4}*16
   88-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {44,16}*1408a, {22,32}*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)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)
( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)
( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)( 69, 76)
( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)
( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)(103,108)
(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)(123,132)
(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)(137,140)
(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)(157,164)
(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)(171,172);;
s1 := (  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)( 15, 21)
( 16, 20)( 17, 19)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)( 28, 41)
( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 45, 68)( 46, 67)( 47, 77)
( 48, 76)( 49, 75)( 50, 74)( 51, 73)( 52, 72)( 53, 71)( 54, 70)( 55, 69)
( 56, 79)( 57, 78)( 58, 88)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 83)
( 64, 82)( 65, 81)( 66, 80)( 89,134)( 90,133)( 91,143)( 92,142)( 93,141)
( 94,140)( 95,139)( 96,138)( 97,137)( 98,136)( 99,135)(100,145)(101,144)
(102,154)(103,153)(104,152)(105,151)(106,150)(107,149)(108,148)(109,147)
(110,146)(111,167)(112,166)(113,176)(114,175)(115,174)(116,173)(117,172)
(118,171)(119,170)(120,169)(121,168)(122,156)(123,155)(124,165)(125,164)
(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157);;
s2 := (  1, 89)(  2, 90)(  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)( 23,122)( 24,123)
( 25,124)( 26,125)( 27,126)( 28,127)( 29,128)( 30,129)( 31,130)( 32,131)
( 33,132)( 34,111)( 35,112)( 36,113)( 37,114)( 38,115)( 39,116)( 40,117)
( 41,118)( 42,119)( 43,120)( 44,121)( 45,155)( 46,156)( 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)( 67,133)( 68,134)( 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);;
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*s0*s1*s2*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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(176)!(  2, 11)(  3, 10)(  4,  9)(  5,  8)(  6,  7)( 13, 22)( 14, 21)
( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)
( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 68, 77)
( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79, 88)( 80, 87)( 81, 86)( 82, 85)
( 83, 84)( 90, 99)( 91, 98)( 92, 97)( 93, 96)( 94, 95)(101,110)(102,109)
(103,108)(104,107)(105,106)(112,121)(113,120)(114,119)(115,118)(116,117)
(123,132)(124,131)(125,130)(126,129)(127,128)(134,143)(135,142)(136,141)
(137,140)(138,139)(145,154)(146,153)(147,152)(148,151)(149,150)(156,165)
(157,164)(158,163)(159,162)(160,161)(167,176)(168,175)(169,174)(170,173)
(171,172);
s1 := Sym(176)!(  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)
( 15, 21)( 16, 20)( 17, 19)( 23, 35)( 24, 34)( 25, 44)( 26, 43)( 27, 42)
( 28, 41)( 29, 40)( 30, 39)( 31, 38)( 32, 37)( 33, 36)( 45, 68)( 46, 67)
( 47, 77)( 48, 76)( 49, 75)( 50, 74)( 51, 73)( 52, 72)( 53, 71)( 54, 70)
( 55, 69)( 56, 79)( 57, 78)( 58, 88)( 59, 87)( 60, 86)( 61, 85)( 62, 84)
( 63, 83)( 64, 82)( 65, 81)( 66, 80)( 89,134)( 90,133)( 91,143)( 92,142)
( 93,141)( 94,140)( 95,139)( 96,138)( 97,137)( 98,136)( 99,135)(100,145)
(101,144)(102,154)(103,153)(104,152)(105,151)(106,150)(107,149)(108,148)
(109,147)(110,146)(111,167)(112,166)(113,176)(114,175)(115,174)(116,173)
(117,172)(118,171)(119,170)(120,169)(121,168)(122,156)(123,155)(124,165)
(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)(131,158)(132,157);
s2 := Sym(176)!(  1, 89)(  2, 90)(  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)( 23,122)
( 24,123)( 25,124)( 26,125)( 27,126)( 28,127)( 29,128)( 30,129)( 31,130)
( 32,131)( 33,132)( 34,111)( 35,112)( 36,113)( 37,114)( 38,115)( 39,116)
( 40,117)( 41,118)( 42,119)( 43,120)( 44,121)( 45,155)( 46,156)( 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)( 67,133)( 68,134)( 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);
poly := sub<Sym(176)|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*s0*s1*s2*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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope