Polytope of Type {2,22,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,22,14}*1232
if this polytope has a name.
Group : SmallGroup(1232,149)
Rank : 4
Schlafli Type : {2,22,14}
Number of vertices, edges, etc : 2, 22, 154, 14
Order of s₀s₁s₂s₃ : 154
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) :
   7-fold quotients : {2,22,2}*176
   11-fold quotients : {2,2,14}*112
   14-fold quotients : {2,11,2}*88
   22-fold quotients : {2,2,7}*56
   77-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope