Polytope of Type {2,14,22}

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

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

Permutation Representation (Magma) :

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

to this polytope