Polytope of Type {2,14,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,28}*1568c
if this polytope has a name.
Group : SmallGroup(1568,877)
Rank : 4
Schlafli Type : {2,14,28}
Number of vertices, edges, etc : 2, 14, 196, 28
Order of s₀s₁s₂s₃ : 28
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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 : {2,14,4}*224
   14-fold quotients : {2,14,2}*112
   28-fold quotients : {2,7,2}*56
   49-fold quotients : {2,2,4}*32
   98-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 10, 45)( 11, 51)( 12, 50)( 13, 49)( 14, 48)
( 15, 47)( 16, 46)( 17, 38)( 18, 44)( 19, 43)( 20, 42)( 21, 41)( 22, 40)
( 23, 39)( 24, 31)( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)( 30, 32)
( 53, 58)( 54, 57)( 55, 56)( 59, 94)( 60,100)( 61, 99)( 62, 98)( 63, 97)
( 64, 96)( 65, 95)( 66, 87)( 67, 93)( 68, 92)( 69, 91)( 70, 90)( 71, 89)
( 72, 88)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)( 79, 81)
(102,107)(103,106)(104,105)(108,143)(109,149)(110,148)(111,147)(112,146)
(113,145)(114,144)(115,136)(116,142)(117,141)(118,140)(119,139)(120,138)
(121,137)(122,129)(123,135)(124,134)(125,133)(126,132)(127,131)(128,130)
(151,156)(152,155)(153,154)(157,192)(158,198)(159,197)(160,196)(161,195)
(162,194)(163,193)(164,185)(165,191)(166,190)(167,189)(168,188)(169,187)
(170,186)(171,178)(172,184)(173,183)(174,182)(175,181)(176,180)(177,179);;
s2 := (  3,109)(  4,108)(  5,114)(  6,113)(  7,112)(  8,111)(  9,110)( 10,102)
( 11,101)( 12,107)( 13,106)( 14,105)( 15,104)( 16,103)( 17,144)( 18,143)
( 19,149)( 20,148)( 21,147)( 22,146)( 23,145)( 24,137)( 25,136)( 26,142)
( 27,141)( 28,140)( 29,139)( 30,138)( 31,130)( 32,129)( 33,135)( 34,134)
( 35,133)( 36,132)( 37,131)( 38,123)( 39,122)( 40,128)( 41,127)( 42,126)
( 43,125)( 44,124)( 45,116)( 46,115)( 47,121)( 48,120)( 49,119)( 50,118)
( 51,117)( 52,158)( 53,157)( 54,163)( 55,162)( 56,161)( 57,160)( 58,159)
( 59,151)( 60,150)( 61,156)( 62,155)( 63,154)( 64,153)( 65,152)( 66,193)
( 67,192)( 68,198)( 69,197)( 70,196)( 71,195)( 72,194)( 73,186)( 74,185)
( 75,191)( 76,190)( 77,189)( 78,188)( 79,187)( 80,179)( 81,178)( 82,184)
( 83,183)( 84,182)( 85,181)( 86,180)( 87,172)( 88,171)( 89,177)( 90,176)
( 91,175)( 92,174)( 93,173)( 94,165)( 95,164)( 96,170)( 97,169)( 98,168)
( 99,167)(100,166);;
s3 := (  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)( 19, 22)
( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)( 39, 44)
( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)( 55, 56)
( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)( 75, 78)
( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)( 95,100)
( 96, 99)( 97, 98)(101,150)(102,156)(103,155)(104,154)(105,153)(106,152)
(107,151)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)(114,158)
(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,171)
(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,178)(130,184)
(131,183)(132,182)(133,181)(134,180)(135,179)(136,185)(137,191)(138,190)
(139,189)(140,188)(141,187)(142,186)(143,192)(144,198)(145,197)(146,196)
(147,195)(148,194)(149,193);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(198)!(1,2);
s1 := Sym(198)!(  4,  9)(  5,  8)(  6,  7)( 10, 45)( 11, 51)( 12, 50)( 13, 49)
( 14, 48)( 15, 47)( 16, 46)( 17, 38)( 18, 44)( 19, 43)( 20, 42)( 21, 41)
( 22, 40)( 23, 39)( 24, 31)( 25, 37)( 26, 36)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 53, 58)( 54, 57)( 55, 56)( 59, 94)( 60,100)( 61, 99)( 62, 98)
( 63, 97)( 64, 96)( 65, 95)( 66, 87)( 67, 93)( 68, 92)( 69, 91)( 70, 90)
( 71, 89)( 72, 88)( 73, 80)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)
( 79, 81)(102,107)(103,106)(104,105)(108,143)(109,149)(110,148)(111,147)
(112,146)(113,145)(114,144)(115,136)(116,142)(117,141)(118,140)(119,139)
(120,138)(121,137)(122,129)(123,135)(124,134)(125,133)(126,132)(127,131)
(128,130)(151,156)(152,155)(153,154)(157,192)(158,198)(159,197)(160,196)
(161,195)(162,194)(163,193)(164,185)(165,191)(166,190)(167,189)(168,188)
(169,187)(170,186)(171,178)(172,184)(173,183)(174,182)(175,181)(176,180)
(177,179);
s2 := Sym(198)!(  3,109)(  4,108)(  5,114)(  6,113)(  7,112)(  8,111)(  9,110)
( 10,102)( 11,101)( 12,107)( 13,106)( 14,105)( 15,104)( 16,103)( 17,144)
( 18,143)( 19,149)( 20,148)( 21,147)( 22,146)( 23,145)( 24,137)( 25,136)
( 26,142)( 27,141)( 28,140)( 29,139)( 30,138)( 31,130)( 32,129)( 33,135)
( 34,134)( 35,133)( 36,132)( 37,131)( 38,123)( 39,122)( 40,128)( 41,127)
( 42,126)( 43,125)( 44,124)( 45,116)( 46,115)( 47,121)( 48,120)( 49,119)
( 50,118)( 51,117)( 52,158)( 53,157)( 54,163)( 55,162)( 56,161)( 57,160)
( 58,159)( 59,151)( 60,150)( 61,156)( 62,155)( 63,154)( 64,153)( 65,152)
( 66,193)( 67,192)( 68,198)( 69,197)( 70,196)( 71,195)( 72,194)( 73,186)
( 74,185)( 75,191)( 76,190)( 77,189)( 78,188)( 79,187)( 80,179)( 81,178)
( 82,184)( 83,183)( 84,182)( 85,181)( 86,180)( 87,172)( 88,171)( 89,177)
( 90,176)( 91,175)( 92,174)( 93,173)( 94,165)( 95,164)( 96,170)( 97,169)
( 98,168)( 99,167)(100,166);
s3 := Sym(198)!(  4,  9)(  5,  8)(  6,  7)( 11, 16)( 12, 15)( 13, 14)( 18, 23)
( 19, 22)( 20, 21)( 25, 30)( 26, 29)( 27, 28)( 32, 37)( 33, 36)( 34, 35)
( 39, 44)( 40, 43)( 41, 42)( 46, 51)( 47, 50)( 48, 49)( 53, 58)( 54, 57)
( 55, 56)( 60, 65)( 61, 64)( 62, 63)( 67, 72)( 68, 71)( 69, 70)( 74, 79)
( 75, 78)( 76, 77)( 81, 86)( 82, 85)( 83, 84)( 88, 93)( 89, 92)( 90, 91)
( 95,100)( 96, 99)( 97, 98)(101,150)(102,156)(103,155)(104,154)(105,153)
(106,152)(107,151)(108,157)(109,163)(110,162)(111,161)(112,160)(113,159)
(114,158)(115,164)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)
(122,171)(123,177)(124,176)(125,175)(126,174)(127,173)(128,172)(129,178)
(130,184)(131,183)(132,182)(133,181)(134,180)(135,179)(136,185)(137,191)
(138,190)(139,189)(140,188)(141,187)(142,186)(143,192)(144,198)(145,197)
(146,196)(147,195)(148,194)(149,193);
poly := sub<Sym(198)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, 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 >;

to this polytope