Polytope of Type {8,44}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,44}*1408b
if this polytope has a name.
Group : SmallGroup(1408,6496)
Rank : 3
Schlafli Type : {8,44}
Number of vertices, edges, etc : 16, 352, 88
Order of s0s1s2 : 44
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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) :
   2-fold quotients : {4,44}*704
   4-fold quotients : {4,44}*352
   8-fold quotients : {2,44}*176, {4,22}*176
   11-fold quotients : {8,4}*128b
   16-fold quotients : {2,22}*88
   22-fold quotients : {4,4}*64
   32-fold quotients : {2,11}*44
   44-fold quotients : {4,4}*32
   88-fold quotients : {2,4}*16, {4,2}*16
   176-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      44 facets:
         44 of {8}*16
      8 vertex figures:
         8 of {44}*88

Permutation Representation (GAP) : 
s0 := (  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)( 23,111)( 24,112)( 25,113)( 26,114)( 27,115)( 28,116)( 29,117)( 30,118)( 31,119)( 32,120)( 33,121)( 34,122)( 35,123)( 36,124)( 37,125)( 38,126)( 39,127)( 40,128)( 41,129)( 42,130)( 43,131)( 44,132)( 45,166)( 46,167)( 47,168)( 48,169)( 49,170)( 50,171)( 51,172)( 52,173)( 53,174)( 54,175)( 55,176)( 56,155)( 57,156)( 58,157)( 59,158)( 60,159)( 61,160)( 62,161)( 63,162)( 64,163)( 65,164)( 66,165)( 67,144)( 68,145)( 69,146)( 70,147)( 71,148)( 72,149)( 73,150)( 74,151)( 75,152)( 76,153)( 77,154)( 78,133)( 79,134)( 80,135)( 81,136)( 82,137)( 83,138)( 84,139)( 85,140)( 86,141)( 87,142)( 88,143);;
s1 := (  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)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 67, 78)( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 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);;
s2 := (  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 79)( 46, 78)( 47, 88)( 48, 87)( 49, 86)( 50, 85)( 51, 84)( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 68)( 57, 67)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)(103,109)(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)(122,123)(124,132)(125,131)(126,130)(127,129)(133,167)(134,166)(135,176)(136,175)(137,174)(138,173)(139,172)(140,171)(141,170)(142,169)(143,168)(144,156)(145,155)(146,165)(147,164)(148,163)(149,162)(150,161)(151,160)(152,159)(153,158)(154,157);;
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*s1*s0*s1*s0*s2*s1*s0*s2*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*s0*s1*s0*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := 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)( 23,111)( 24,112)( 25,113)( 26,114)( 27,115)( 28,116)( 29,117)( 30,118)( 31,119)( 32,120)( 33,121)( 34,122)( 35,123)( 36,124)( 37,125)( 38,126)( 39,127)( 40,128)( 41,129)( 42,130)( 43,131)( 44,132)( 45,166)( 46,167)( 47,168)( 48,169)( 49,170)( 50,171)( 51,172)( 52,173)( 53,174)( 54,175)( 55,176)( 56,155)( 57,156)( 58,157)( 59,158)( 60,159)( 61,160)( 62,161)( 63,162)( 64,163)( 65,164)( 66,165)( 67,144)( 68,145)( 69,146)( 70,147)( 71,148)( 72,149)( 73,150)( 74,151)( 75,152)( 76,153)( 77,154)( 78,133)( 79,134)( 80,135)( 81,136)( 82,137)( 83,138)( 84,139)( 85,140)( 86,141)( 87,142)( 88,143);
s1 := Sym(176)!(  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)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 67, 78)( 68, 88)( 69, 87)( 70, 86)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 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);
s2 := Sym(176)!(  1,  2)(  3, 11)(  4, 10)(  5,  9)(  6,  8)( 12, 13)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 45, 79)( 46, 78)( 47, 88)( 48, 87)( 49, 86)( 50, 85)( 51, 84)( 52, 83)( 53, 82)( 54, 81)( 55, 80)( 56, 68)( 57, 67)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,101)(102,110)(103,109)(104,108)(105,107)(111,112)(113,121)(114,120)(115,119)(116,118)(122,123)(124,132)(125,131)(126,130)(127,129)(133,167)(134,166)(135,176)(136,175)(137,174)(138,173)(139,172)(140,171)(141,170)(142,169)(143,168)(144,156)(145,155)(146,165)(147,164)(148,163)(149,162)(150,161)(151,160)(152,159)(153,158)(154,157);
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*s2*s1*s0*s1*s0*s2*s1*s0*s2*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*s0*s1*s0*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*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
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