Polytope of Type {14,4,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,4,14}*1568
Also Known As : {{14,4|2},{4,14|2}}. if this polytope has another name.
Group : SmallGroup(1568,858)
Rank : 4
Schlafli Type : {14,4,14}
Number of vertices, edges, etc : 14, 28, 28, 14
Order of s₀s₁s₂s₃ : 28
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
   Self-Dual
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 : {14,2,14}*784
   4-fold quotients : {7,2,14}*392, {14,2,7}*392
   7-fold quotients : {2,4,14}*224, {14,4,2}*224
   8-fold quotients : {7,2,7}*196
   14-fold quotients : {2,2,14}*112, {14,2,2}*112
   28-fold quotients : {2,2,7}*56, {7,2,2}*56
   49-fold quotients : {2,4,2}*32
   98-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope