Polytope of Type {4,14,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,14,14}*1568b
if this polytope has a name.
Group : SmallGroup(1568,858)
Rank : 4
Schlafli Type : {4,14,14}
Number of vertices, edges, etc : 4, 28, 98, 14
Order of s₀s₁s₂s₃ : 28
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {2,14,14}*784c
   4-fold quotients : {2,7,14}*392
   7-fold quotients : {4,14,2}*224
   14-fold quotients : {2,14,2}*112
   28-fold quotients : {2,7,2}*56
   49-fold quotients : {4,2,2}*32
   98-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)(106,155)
(107,156)(108,157)(109,158)(110,159)(111,160)(112,161)(113,162)(114,163)
(115,164)(116,165)(117,166)(118,167)(119,168)(120,169)(121,170)(122,171)
(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)(130,179)
(131,180)(132,181)(133,182)(134,183)(135,184)(136,185)(137,186)(138,187)
(139,188)(140,189)(141,190)(142,191)(143,192)(144,193)(145,194)(146,195)
(147,196);;
s1 := (  1, 99)(  2,105)(  3,104)(  4,103)(  5,102)(  6,101)(  7,100)(  8,141)
(  9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,134)( 16,140)
( 17,139)( 18,138)( 19,137)( 20,136)( 21,135)( 22,127)( 23,133)( 24,132)
( 25,131)( 26,130)( 27,129)( 28,128)( 29,120)( 30,126)( 31,125)( 32,124)
( 33,123)( 34,122)( 35,121)( 36,113)( 37,119)( 38,118)( 39,117)( 40,116)
( 41,115)( 42,114)( 43,106)( 44,112)( 45,111)( 46,110)( 47,109)( 48,108)
( 49,107)( 50,148)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)
( 57,190)( 58,196)( 59,195)( 60,194)( 61,193)( 62,192)( 63,191)( 64,183)
( 65,189)( 66,188)( 67,187)( 68,186)( 69,185)( 70,184)( 71,176)( 72,182)
( 73,181)( 74,180)( 75,179)( 76,178)( 77,177)( 78,169)( 79,175)( 80,174)
( 81,173)( 82,172)( 83,171)( 84,170)( 85,162)( 86,168)( 87,167)( 88,166)
( 89,165)( 90,164)( 91,163)( 92,155)( 93,161)( 94,160)( 95,159)( 96,158)
( 97,157)( 98,156);;
s2 := (  1,  9)(  2,  8)(  3, 14)(  4, 13)(  5, 12)(  6, 11)(  7, 10)( 15, 44)
( 16, 43)( 17, 49)( 18, 48)( 19, 47)( 20, 46)( 21, 45)( 22, 37)( 23, 36)
( 24, 42)( 25, 41)( 26, 40)( 27, 39)( 28, 38)( 29, 30)( 31, 35)( 32, 34)
( 50, 58)( 51, 57)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)( 64, 93)
( 65, 92)( 66, 98)( 67, 97)( 68, 96)( 69, 95)( 70, 94)( 71, 86)( 72, 85)
( 73, 91)( 74, 90)( 75, 89)( 76, 88)( 77, 87)( 78, 79)( 80, 84)( 81, 83)
( 99,107)(100,106)(101,112)(102,111)(103,110)(104,109)(105,108)(113,142)
(114,141)(115,147)(116,146)(117,145)(118,144)(119,143)(120,135)(121,134)
(122,140)(123,139)(124,138)(125,137)(126,136)(127,128)(129,133)(130,132)
(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)(154,157)(162,191)
(163,190)(164,196)(165,195)(166,194)(167,193)(168,192)(169,184)(170,183)
(171,189)(172,188)(173,187)(174,186)(175,185)(176,177)(178,182)(179,181);;
s3 := (  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 36)
( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)( 23, 30)
( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 57, 92)( 58, 93)( 59, 94)
( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)( 67, 88)
( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)( 75, 82)
( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)(111,146)
(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)(119,140)
(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)(155,190)
(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)(163,184)
(164,185)(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)(171,178)
(172,179)(173,180)(174,181)(175,182);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s3*s1*s2*s3*s2*s3*s1*s2*s3*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(196)!( 99,148)(100,149)(101,150)(102,151)(103,152)(104,153)(105,154)
(106,155)(107,156)(108,157)(109,158)(110,159)(111,160)(112,161)(113,162)
(114,163)(115,164)(116,165)(117,166)(118,167)(119,168)(120,169)(121,170)
(122,171)(123,172)(124,173)(125,174)(126,175)(127,176)(128,177)(129,178)
(130,179)(131,180)(132,181)(133,182)(134,183)(135,184)(136,185)(137,186)
(138,187)(139,188)(140,189)(141,190)(142,191)(143,192)(144,193)(145,194)
(146,195)(147,196);
s1 := Sym(196)!(  1, 99)(  2,105)(  3,104)(  4,103)(  5,102)(  6,101)(  7,100)
(  8,141)(  9,147)( 10,146)( 11,145)( 12,144)( 13,143)( 14,142)( 15,134)
( 16,140)( 17,139)( 18,138)( 19,137)( 20,136)( 21,135)( 22,127)( 23,133)
( 24,132)( 25,131)( 26,130)( 27,129)( 28,128)( 29,120)( 30,126)( 31,125)
( 32,124)( 33,123)( 34,122)( 35,121)( 36,113)( 37,119)( 38,118)( 39,117)
( 40,116)( 41,115)( 42,114)( 43,106)( 44,112)( 45,111)( 46,110)( 47,109)
( 48,108)( 49,107)( 50,148)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)
( 56,149)( 57,190)( 58,196)( 59,195)( 60,194)( 61,193)( 62,192)( 63,191)
( 64,183)( 65,189)( 66,188)( 67,187)( 68,186)( 69,185)( 70,184)( 71,176)
( 72,182)( 73,181)( 74,180)( 75,179)( 76,178)( 77,177)( 78,169)( 79,175)
( 80,174)( 81,173)( 82,172)( 83,171)( 84,170)( 85,162)( 86,168)( 87,167)
( 88,166)( 89,165)( 90,164)( 91,163)( 92,155)( 93,161)( 94,160)( 95,159)
( 96,158)( 97,157)( 98,156);
s2 := Sym(196)!(  1,  9)(  2,  8)(  3, 14)(  4, 13)(  5, 12)(  6, 11)(  7, 10)
( 15, 44)( 16, 43)( 17, 49)( 18, 48)( 19, 47)( 20, 46)( 21, 45)( 22, 37)
( 23, 36)( 24, 42)( 25, 41)( 26, 40)( 27, 39)( 28, 38)( 29, 30)( 31, 35)
( 32, 34)( 50, 58)( 51, 57)( 52, 63)( 53, 62)( 54, 61)( 55, 60)( 56, 59)
( 64, 93)( 65, 92)( 66, 98)( 67, 97)( 68, 96)( 69, 95)( 70, 94)( 71, 86)
( 72, 85)( 73, 91)( 74, 90)( 75, 89)( 76, 88)( 77, 87)( 78, 79)( 80, 84)
( 81, 83)( 99,107)(100,106)(101,112)(102,111)(103,110)(104,109)(105,108)
(113,142)(114,141)(115,147)(116,146)(117,145)(118,144)(119,143)(120,135)
(121,134)(122,140)(123,139)(124,138)(125,137)(126,136)(127,128)(129,133)
(130,132)(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)(154,157)
(162,191)(163,190)(164,196)(165,195)(166,194)(167,193)(168,192)(169,184)
(170,183)(171,189)(172,188)(173,187)(174,186)(175,185)(176,177)(178,182)
(179,181);
s3 := Sym(196)!(  8, 43)(  9, 44)( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)
( 15, 36)( 16, 37)( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 29)
( 23, 30)( 24, 31)( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 57, 92)( 58, 93)
( 59, 94)( 60, 95)( 61, 96)( 62, 97)( 63, 98)( 64, 85)( 65, 86)( 66, 87)
( 67, 88)( 68, 89)( 69, 90)( 70, 91)( 71, 78)( 72, 79)( 73, 80)( 74, 81)
( 75, 82)( 76, 83)( 77, 84)(106,141)(107,142)(108,143)(109,144)(110,145)
(111,146)(112,147)(113,134)(114,135)(115,136)(116,137)(117,138)(118,139)
(119,140)(120,127)(121,128)(122,129)(123,130)(124,131)(125,132)(126,133)
(155,190)(156,191)(157,192)(158,193)(159,194)(160,195)(161,196)(162,183)
(163,184)(164,185)(165,186)(166,187)(167,188)(168,189)(169,176)(170,177)
(171,178)(172,179)(173,180)(174,181)(175,182);
poly := sub<Sym(196)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*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*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope