Polytope of Type {2,3,12,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,3,12,6}*1152
if this polytope has a name.
Group : SmallGroup(1152,157603)
Rank : 5
Schlafli Type : {2,3,12,6}
Number of vertices, edges, etc : 2, 4, 24, 48, 6
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 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 : {2,3,6,6}*576
3-fold quotients : {2,3,12,2}*384
6-fold quotients : {2,3,6,2}*192
12-fold quotients : {2,3,3,2}*96
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 5, 8)( 6, 7)( 9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)( 22, 23)
( 25, 26)( 27, 51)( 28, 52)( 29, 56)( 30, 55)( 31, 54)( 32, 53)( 33, 58)
( 34, 57)( 35, 59)( 36, 60)( 37, 64)( 38, 63)( 39, 62)( 40, 61)( 41, 66)
( 42, 65)( 43, 67)( 44, 68)( 45, 72)( 46, 71)( 47, 70)( 48, 69)( 49, 74)
( 50, 73)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)( 91, 92)
( 93, 95)( 94, 96)( 99,124)(100,123)(101,127)(102,128)(103,125)(104,126)
(105,129)(106,130)(107,132)(108,131)(109,135)(110,136)(111,133)(112,134)
(113,137)(114,138)(115,140)(116,139)(117,143)(118,144)(119,141)(120,142)
(121,145)(122,146);;
s2 := ( 3, 27)( 4, 28)( 5, 30)( 6, 29)( 7, 33)( 8, 34)( 9, 31)( 10, 32)
( 11, 35)( 12, 36)( 13, 38)( 14, 37)( 15, 41)( 16, 42)( 17, 39)( 18, 40)
( 19, 43)( 20, 44)( 21, 46)( 22, 45)( 23, 49)( 24, 50)( 25, 47)( 26, 48)
( 53, 54)( 55, 57)( 56, 58)( 61, 62)( 63, 65)( 64, 66)( 69, 70)( 71, 73)
( 72, 74)( 75,100)( 76, 99)( 77,101)( 78,102)( 79,106)( 80,105)( 81,104)
( 82,103)( 83,108)( 84,107)( 85,109)( 86,110)( 87,114)( 88,113)( 89,112)
( 90,111)( 91,116)( 92,115)( 93,117)( 94,118)( 95,122)( 96,121)( 97,120)
( 98,119)(123,124)(127,130)(128,129)(131,132)(135,138)(136,137)(139,140)
(143,146)(144,145);;
s3 := ( 3, 81)( 4, 82)( 5, 77)( 6, 78)( 7, 80)( 8, 79)( 9, 75)( 10, 76)
( 11, 97)( 12, 98)( 13, 93)( 14, 94)( 15, 96)( 16, 95)( 17, 91)( 18, 92)
( 19, 89)( 20, 90)( 21, 85)( 22, 86)( 23, 88)( 24, 87)( 25, 83)( 26, 84)
( 27,129)( 28,130)( 29,125)( 30,126)( 31,128)( 32,127)( 33,123)( 34,124)
( 35,145)( 36,146)( 37,141)( 38,142)( 39,144)( 40,143)( 41,139)( 42,140)
( 43,137)( 44,138)( 45,133)( 46,134)( 47,136)( 48,135)( 49,131)( 50,132)
( 51,105)( 52,106)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 99)( 58,100)
( 59,121)( 60,122)( 61,117)( 62,118)( 63,120)( 64,119)( 65,115)( 66,116)
( 67,113)( 68,114)( 69,109)( 70,110)( 71,112)( 72,111)( 73,107)( 74,108);;
s4 := ( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)( 10, 18)
( 27, 35)( 28, 36)( 29, 37)( 30, 38)( 31, 39)( 32, 40)( 33, 41)( 34, 42)
( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)( 58, 66)
( 75, 83)( 76, 84)( 77, 85)( 78, 86)( 79, 87)( 80, 88)( 81, 89)( 82, 90)
( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)(106,114)
(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)(129,137)(130,138);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 5, 8)( 6, 7)( 9, 10)( 13, 16)( 14, 15)( 17, 18)( 21, 24)
( 22, 23)( 25, 26)( 27, 51)( 28, 52)( 29, 56)( 30, 55)( 31, 54)( 32, 53)
( 33, 58)( 34, 57)( 35, 59)( 36, 60)( 37, 64)( 38, 63)( 39, 62)( 40, 61)
( 41, 66)( 42, 65)( 43, 67)( 44, 68)( 45, 72)( 46, 71)( 47, 70)( 48, 69)
( 49, 74)( 50, 73)( 75, 76)( 77, 79)( 78, 80)( 83, 84)( 85, 87)( 86, 88)
( 91, 92)( 93, 95)( 94, 96)( 99,124)(100,123)(101,127)(102,128)(103,125)
(104,126)(105,129)(106,130)(107,132)(108,131)(109,135)(110,136)(111,133)
(112,134)(113,137)(114,138)(115,140)(116,139)(117,143)(118,144)(119,141)
(120,142)(121,145)(122,146);
s2 := Sym(146)!( 3, 27)( 4, 28)( 5, 30)( 6, 29)( 7, 33)( 8, 34)( 9, 31)
( 10, 32)( 11, 35)( 12, 36)( 13, 38)( 14, 37)( 15, 41)( 16, 42)( 17, 39)
( 18, 40)( 19, 43)( 20, 44)( 21, 46)( 22, 45)( 23, 49)( 24, 50)( 25, 47)
( 26, 48)( 53, 54)( 55, 57)( 56, 58)( 61, 62)( 63, 65)( 64, 66)( 69, 70)
( 71, 73)( 72, 74)( 75,100)( 76, 99)( 77,101)( 78,102)( 79,106)( 80,105)
( 81,104)( 82,103)( 83,108)( 84,107)( 85,109)( 86,110)( 87,114)( 88,113)
( 89,112)( 90,111)( 91,116)( 92,115)( 93,117)( 94,118)( 95,122)( 96,121)
( 97,120)( 98,119)(123,124)(127,130)(128,129)(131,132)(135,138)(136,137)
(139,140)(143,146)(144,145);
s3 := Sym(146)!( 3, 81)( 4, 82)( 5, 77)( 6, 78)( 7, 80)( 8, 79)( 9, 75)
( 10, 76)( 11, 97)( 12, 98)( 13, 93)( 14, 94)( 15, 96)( 16, 95)( 17, 91)
( 18, 92)( 19, 89)( 20, 90)( 21, 85)( 22, 86)( 23, 88)( 24, 87)( 25, 83)
( 26, 84)( 27,129)( 28,130)( 29,125)( 30,126)( 31,128)( 32,127)( 33,123)
( 34,124)( 35,145)( 36,146)( 37,141)( 38,142)( 39,144)( 40,143)( 41,139)
( 42,140)( 43,137)( 44,138)( 45,133)( 46,134)( 47,136)( 48,135)( 49,131)
( 50,132)( 51,105)( 52,106)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 99)
( 58,100)( 59,121)( 60,122)( 61,117)( 62,118)( 63,120)( 64,119)( 65,115)
( 66,116)( 67,113)( 68,114)( 69,109)( 70,110)( 71,112)( 72,111)( 73,107)
( 74,108);
s4 := Sym(146)!( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 9, 17)
( 10, 18)( 27, 35)( 28, 36)( 29, 37)( 30, 38)( 31, 39)( 32, 40)( 33, 41)
( 34, 42)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 57, 65)
( 58, 66)( 75, 83)( 76, 84)( 77, 85)( 78, 86)( 79, 87)( 80, 88)( 81, 89)
( 82, 90)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(105,113)
(106,114)(123,131)(124,132)(125,133)(126,134)(127,135)(128,136)(129,137)
(130,138);
poly := sub<Sym(146)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2,
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2 >;
to this polytope