Polytope of Type {4,28}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,28}*1568
if this polytope has a name.
Group : SmallGroup(1568,821)
Rank : 3
Schlafli Type : {4,28}
Number of vertices, edges, etc : 28, 392, 196
Order of s0s1s2 : 4
Order of s0s1s2s1 : 14
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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) :
   2-fold quotients : {4,14}*784
   4-fold quotients : {4,14}*392
   49-fold quotients : {4,4}*32
   98-fold quotients : {2,4}*16, {4,2}*16
   196-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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      98 facets:
         98 of {4}*8
      14 vertex figures:
         14 of {28}*56
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 7.
      28 facets:
         28 of {4}*8
      4 vertex figures:
         4 of {28}*56
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 7.
      28 facets:
         28 of {4}*8
      4 vertex figures:
         4 of {28}*56
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s2> of order 7.
      28 facets:
         28 of {4}*8
      16 vertex figures:
         2 of {28}*56
         14 of {4}*8

Permutation Representation (GAP) : 
s0 := (  2, 44)(  3, 38)(  4, 32)(  5, 26)(  6, 20)(  7, 14)(  8, 43)(  9, 37)( 10, 31)( 11, 25)( 12, 19)( 15, 36)( 16, 30)( 17, 24)( 21, 49)( 22, 29)( 27, 48)( 28, 42)( 33, 47)( 34, 41)( 39, 46)( 51, 93)( 52, 87)( 53, 81)( 54, 75)( 55, 69)( 56, 63)( 57, 92)( 58, 86)( 59, 80)( 60, 74)( 61, 68)( 64, 85)( 65, 79)( 66, 73)( 70, 98)( 71, 78)( 76, 97)( 77, 91)( 82, 96)( 83, 90)( 88, 95)(100,142)(101,136)(102,130)(103,124)(104,118)(105,112)(106,141)(107,135)(108,129)(109,123)(110,117)(113,134)(114,128)(115,122)(119,147)(120,127)(125,146)(126,140)(131,145)(132,139)(137,144)(149,191)(150,185)(151,179)(152,173)(153,167)(154,161)(155,190)(156,184)(157,178)(158,172)(159,166)(162,183)(163,177)(164,171)(168,196)(169,176)(174,195)(175,189)(180,194)(181,188)(186,193);;
s1 := (  8, 45)(  9, 46)( 10, 47)( 11, 48)( 12, 49)( 13, 43)( 14, 44)( 15, 40)( 16, 41)( 17, 42)( 18, 36)( 19, 37)( 20, 38)( 21, 39)( 22, 35)( 23, 29)( 24, 30)( 25, 31)( 26, 32)( 27, 33)( 28, 34)( 57, 94)( 58, 95)( 59, 96)( 60, 97)( 61, 98)( 62, 92)( 63, 93)( 64, 89)( 65, 90)( 66, 91)( 67, 85)( 68, 86)( 69, 87)( 70, 88)( 71, 84)( 72, 78)( 73, 79)( 74, 80)( 75, 81)( 76, 82)( 77, 83)( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)(106,192)(107,193)(108,194)(109,195)(110,196)(111,190)(112,191)(113,187)(114,188)(115,189)(116,183)(117,184)(118,185)(119,186)(120,182)(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,170)(128,171)(129,172)(130,173)(131,174)(132,175)(133,169)(134,165)(135,166)(136,167)(137,168)(138,162)(139,163)(140,164)(141,160)(142,161)(143,155)(144,156)(145,157)(146,158)(147,159);;
s2 := (  1,121)(  2,120)(  3,126)(  4,125)(  5,124)(  6,123)(  7,122)(  8,114)(  9,113)( 10,119)( 11,118)( 12,117)( 13,116)( 14,115)( 15,107)( 16,106)( 17,112)( 18,111)( 19,110)( 20,109)( 21,108)( 22,100)( 23, 99)( 24,105)( 25,104)( 26,103)( 27,102)( 28,101)( 29,142)( 30,141)( 31,147)( 32,146)( 33,145)( 34,144)( 35,143)( 36,135)( 37,134)( 38,140)( 39,139)( 40,138)( 41,137)( 42,136)( 43,128)( 44,127)( 45,133)( 46,132)( 47,131)( 48,130)( 49,129)( 50,170)( 51,169)( 52,175)( 53,174)( 54,173)( 55,172)( 56,171)( 57,163)( 58,162)( 59,168)( 60,167)( 61,166)( 62,165)( 63,164)( 64,156)( 65,155)( 66,161)( 67,160)( 68,159)( 69,158)( 70,157)( 71,149)( 72,148)( 73,154)( 74,153)( 75,152)( 76,151)( 77,150)( 78,191)( 79,190)( 80,196)( 81,195)( 82,194)( 83,193)( 84,192)( 85,184)( 86,183)( 87,189)( 88,188)( 89,187)( 90,186)( 91,185)( 92,177)( 93,176)( 94,182)( 95,181)( 96,180)( 97,179)( 98,178);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(196)!(  2, 44)(  3, 38)(  4, 32)(  5, 26)(  6, 20)(  7, 14)(  8, 43)(  9, 37)( 10, 31)( 11, 25)( 12, 19)( 15, 36)( 16, 30)( 17, 24)( 21, 49)( 22, 29)( 27, 48)( 28, 42)( 33, 47)( 34, 41)( 39, 46)( 51, 93)( 52, 87)( 53, 81)( 54, 75)( 55, 69)( 56, 63)( 57, 92)( 58, 86)( 59, 80)( 60, 74)( 61, 68)( 64, 85)( 65, 79)( 66, 73)( 70, 98)( 71, 78)( 76, 97)( 77, 91)( 82, 96)( 83, 90)( 88, 95)(100,142)(101,136)(102,130)(103,124)(104,118)(105,112)(106,141)(107,135)(108,129)(109,123)(110,117)(113,134)(114,128)(115,122)(119,147)(120,127)(125,146)(126,140)(131,145)(132,139)(137,144)(149,191)(150,185)(151,179)(152,173)(153,167)(154,161)(155,190)(156,184)(157,178)(158,172)(159,166)(162,183)(163,177)(164,171)(168,196)(169,176)(174,195)(175,189)(180,194)(181,188)(186,193);
s1 := Sym(196)!(  8, 45)(  9, 46)( 10, 47)( 11, 48)( 12, 49)( 13, 43)( 14, 44)( 15, 40)( 16, 41)( 17, 42)( 18, 36)( 19, 37)( 20, 38)( 21, 39)( 22, 35)( 23, 29)( 24, 30)( 25, 31)( 26, 32)( 27, 33)( 28, 34)( 57, 94)( 58, 95)( 59, 96)( 60, 97)( 61, 98)( 62, 92)( 63, 93)( 64, 89)( 65, 90)( 66, 91)( 67, 85)( 68, 86)( 69, 87)( 70, 88)( 71, 84)( 72, 78)( 73, 79)( 74, 80)( 75, 81)( 76, 82)( 77, 83)( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)(106,192)(107,193)(108,194)(109,195)(110,196)(111,190)(112,191)(113,187)(114,188)(115,189)(116,183)(117,184)(118,185)(119,186)(120,182)(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,170)(128,171)(129,172)(130,173)(131,174)(132,175)(133,169)(134,165)(135,166)(136,167)(137,168)(138,162)(139,163)(140,164)(141,160)(142,161)(143,155)(144,156)(145,157)(146,158)(147,159);
s2 := Sym(196)!(  1,121)(  2,120)(  3,126)(  4,125)(  5,124)(  6,123)(  7,122)(  8,114)(  9,113)( 10,119)( 11,118)( 12,117)( 13,116)( 14,115)( 15,107)( 16,106)( 17,112)( 18,111)( 19,110)( 20,109)( 21,108)( 22,100)( 23, 99)( 24,105)( 25,104)( 26,103)( 27,102)( 28,101)( 29,142)( 30,141)( 31,147)( 32,146)( 33,145)( 34,144)( 35,143)( 36,135)( 37,134)( 38,140)( 39,139)( 40,138)( 41,137)( 42,136)( 43,128)( 44,127)( 45,133)( 46,132)( 47,131)( 48,130)( 49,129)( 50,170)( 51,169)( 52,175)( 53,174)( 54,173)( 55,172)( 56,171)( 57,163)( 58,162)( 59,168)( 60,167)( 61,166)( 62,165)( 63,164)( 64,156)( 65,155)( 66,161)( 67,160)( 68,159)( 69,158)( 70,157)( 71,149)( 72,148)( 73,154)( 74,153)( 75,152)( 76,151)( 77,150)( 78,191)( 79,190)( 80,196)( 81,195)( 82,194)( 83,193)( 84,192)( 85,184)( 86,183)( 87,189)( 88,188)( 89,187)( 90,186)( 91,185)( 92,177)( 93,176)( 94,182)( 95,181)( 96,180)( 97,179)( 98,178);
poly := sub<Sym(196)|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*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;
References : None.
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