Polytope of Type {2,28,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,28,14}*1568a
if this polytope has a name.
Group : SmallGroup(1568,851)
Rank : 4
Schlafli Type : {2,28,14}
Number of vertices, edges, etc : 2, 28, 196, 14
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}*784a
   7-fold quotients : {2,28,2}*224, {2,4,14}*224
   14-fold quotients : {2,2,14}*112, {2,14,2}*112
   28-fold quotients : {2,2,7}*56, {2,7,2}*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 := (1,2);;
s1 := ( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 50)( 16, 51)( 17, 38)
( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 43)( 23, 44)( 24, 31)( 25, 32)
( 26, 33)( 27, 34)( 28, 35)( 29, 36)( 30, 37)( 59, 94)( 60, 95)( 61, 96)
( 62, 97)( 63, 98)( 64, 99)( 65,100)( 66, 87)( 67, 88)( 68, 89)( 69, 90)
( 70, 91)( 71, 92)( 72, 93)( 73, 80)( 74, 81)( 75, 82)( 76, 83)( 77, 84)
( 78, 85)( 79, 86)(101,150)(102,151)(103,152)(104,153)(105,154)(106,155)
(107,156)(108,192)(109,193)(110,194)(111,195)(112,196)(113,197)(114,198)
(115,185)(116,186)(117,187)(118,188)(119,189)(120,190)(121,191)(122,178)
(123,179)(124,180)(125,181)(126,182)(127,183)(128,184)(129,171)(130,172)
(131,173)(132,174)(133,175)(134,176)(135,177)(136,164)(137,165)(138,166)
(139,167)(140,168)(141,169)(142,170)(143,157)(144,158)(145,159)(146,160)
(147,161)(148,162)(149,163);;
s2 := (  3,108)(  4,114)(  5,113)(  6,112)(  7,111)(  8,110)(  9,109)( 10,101)
( 11,107)( 12,106)( 13,105)( 14,104)( 15,103)( 16,102)( 17,143)( 18,149)
( 19,148)( 20,147)( 21,146)( 22,145)( 23,144)( 24,136)( 25,142)( 26,141)
( 27,140)( 28,139)( 29,138)( 30,137)( 31,129)( 32,135)( 33,134)( 34,133)
( 35,132)( 36,131)( 37,130)( 38,122)( 39,128)( 40,127)( 41,126)( 42,125)
( 43,124)( 44,123)( 45,115)( 46,121)( 47,120)( 48,119)( 49,118)( 50,117)
( 51,116)( 52,157)( 53,163)( 54,162)( 55,161)( 56,160)( 57,159)( 58,158)
( 59,150)( 60,156)( 61,155)( 62,154)( 63,153)( 64,152)( 65,151)( 66,192)
( 67,198)( 68,197)( 69,196)( 70,195)( 71,194)( 72,193)( 73,185)( 74,191)
( 75,190)( 76,189)( 77,188)( 78,187)( 79,186)( 80,178)( 81,184)( 82,183)
( 83,182)( 84,181)( 85,180)( 86,179)( 87,171)( 88,177)( 89,176)( 90,175)
( 91,174)( 92,173)( 93,172)( 94,164)( 95,170)( 96,169)( 97,168)( 98,167)
( 99,166)(100,165);;
s3 := (  3,  4)(  5,  9)(  6,  8)( 10, 11)( 12, 16)( 13, 15)( 17, 18)( 19, 23)
( 20, 22)( 24, 25)( 26, 30)( 27, 29)( 31, 32)( 33, 37)( 34, 36)( 38, 39)
( 40, 44)( 41, 43)( 45, 46)( 47, 51)( 48, 50)( 52, 53)( 54, 58)( 55, 57)
( 59, 60)( 61, 65)( 62, 64)( 66, 67)( 68, 72)( 69, 71)( 73, 74)( 75, 79)
( 76, 78)( 80, 81)( 82, 86)( 83, 85)( 87, 88)( 89, 93)( 90, 92)( 94, 95)
( 96,100)( 97, 99)(101,102)(103,107)(104,106)(108,109)(110,114)(111,113)
(115,116)(117,121)(118,120)(122,123)(124,128)(125,127)(129,130)(131,135)
(132,134)(136,137)(138,142)(139,141)(143,144)(145,149)(146,148)(150,151)
(152,156)(153,155)(157,158)(159,163)(160,162)(164,165)(166,170)(167,169)
(171,172)(173,177)(174,176)(178,179)(180,184)(181,183)(185,186)(187,191)
(188,190)(192,193)(194,198)(195,197);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, 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, 
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(198)!(1,2);
s1 := Sym(198)!( 10, 45)( 11, 46)( 12, 47)( 13, 48)( 14, 49)( 15, 50)( 16, 51)
( 17, 38)( 18, 39)( 19, 40)( 20, 41)( 21, 42)( 22, 43)( 23, 44)( 24, 31)
( 25, 32)( 26, 33)( 27, 34)( 28, 35)( 29, 36)( 30, 37)( 59, 94)( 60, 95)
( 61, 96)( 62, 97)( 63, 98)( 64, 99)( 65,100)( 66, 87)( 67, 88)( 68, 89)
( 69, 90)( 70, 91)( 71, 92)( 72, 93)( 73, 80)( 74, 81)( 75, 82)( 76, 83)
( 77, 84)( 78, 85)( 79, 86)(101,150)(102,151)(103,152)(104,153)(105,154)
(106,155)(107,156)(108,192)(109,193)(110,194)(111,195)(112,196)(113,197)
(114,198)(115,185)(116,186)(117,187)(118,188)(119,189)(120,190)(121,191)
(122,178)(123,179)(124,180)(125,181)(126,182)(127,183)(128,184)(129,171)
(130,172)(131,173)(132,174)(133,175)(134,176)(135,177)(136,164)(137,165)
(138,166)(139,167)(140,168)(141,169)(142,170)(143,157)(144,158)(145,159)
(146,160)(147,161)(148,162)(149,163);
s2 := Sym(198)!(  3,108)(  4,114)(  5,113)(  6,112)(  7,111)(  8,110)(  9,109)
( 10,101)( 11,107)( 12,106)( 13,105)( 14,104)( 15,103)( 16,102)( 17,143)
( 18,149)( 19,148)( 20,147)( 21,146)( 22,145)( 23,144)( 24,136)( 25,142)
( 26,141)( 27,140)( 28,139)( 29,138)( 30,137)( 31,129)( 32,135)( 33,134)
( 34,133)( 35,132)( 36,131)( 37,130)( 38,122)( 39,128)( 40,127)( 41,126)
( 42,125)( 43,124)( 44,123)( 45,115)( 46,121)( 47,120)( 48,119)( 49,118)
( 50,117)( 51,116)( 52,157)( 53,163)( 54,162)( 55,161)( 56,160)( 57,159)
( 58,158)( 59,150)( 60,156)( 61,155)( 62,154)( 63,153)( 64,152)( 65,151)
( 66,192)( 67,198)( 68,197)( 69,196)( 70,195)( 71,194)( 72,193)( 73,185)
( 74,191)( 75,190)( 76,189)( 77,188)( 78,187)( 79,186)( 80,178)( 81,184)
( 82,183)( 83,182)( 84,181)( 85,180)( 86,179)( 87,171)( 88,177)( 89,176)
( 90,175)( 91,174)( 92,173)( 93,172)( 94,164)( 95,170)( 96,169)( 97,168)
( 98,167)( 99,166)(100,165);
s3 := Sym(198)!(  3,  4)(  5,  9)(  6,  8)( 10, 11)( 12, 16)( 13, 15)( 17, 18)
( 19, 23)( 20, 22)( 24, 25)( 26, 30)( 27, 29)( 31, 32)( 33, 37)( 34, 36)
( 38, 39)( 40, 44)( 41, 43)( 45, 46)( 47, 51)( 48, 50)( 52, 53)( 54, 58)
( 55, 57)( 59, 60)( 61, 65)( 62, 64)( 66, 67)( 68, 72)( 69, 71)( 73, 74)
( 75, 79)( 76, 78)( 80, 81)( 82, 86)( 83, 85)( 87, 88)( 89, 93)( 90, 92)
( 94, 95)( 96,100)( 97, 99)(101,102)(103,107)(104,106)(108,109)(110,114)
(111,113)(115,116)(117,121)(118,120)(122,123)(124,128)(125,127)(129,130)
(131,135)(132,134)(136,137)(138,142)(139,141)(143,144)(145,149)(146,148)
(150,151)(152,156)(153,155)(157,158)(159,163)(160,162)(164,165)(166,170)
(167,169)(171,172)(173,177)(174,176)(178,179)(180,184)(181,183)(185,186)
(187,191)(188,190)(192,193)(194,198)(195,197);
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, s1*s2*s3*s2*s1*s2*s3*s2, 
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, 
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 >;

to this polytope