Polytope of Type {2,4,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,3}*1152a
if this polytope has a name.
Group : SmallGroup(1152,157640)
Rank : 5
Schlafli Type : {2,4,6,3}
Number of vertices, edges, etc : 2, 4, 48, 36, 12
Order of s0s1s2s3s4 : 12
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 : {2,2,6,3}*576
3-fold quotients : {2,4,6,3}*384
4-fold quotients : {2,4,6,3}*288
6-fold quotients : {2,2,6,3}*192
8-fold quotients : {2,2,6,3}*144
12-fold quotients : {2,4,2,3}*96, {2,2,3,3}*96
24-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)( 10, 82)
( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)( 18, 90)
( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)( 26, 98)
( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)( 34,106)
( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)( 41,113)( 42,114)
( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)( 50,122)
( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)( 57,129)( 58,130)
( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)( 66,138)
( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)( 73,145)( 74,146);;
s2 := ( 4, 5)( 8, 9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)( 19, 31)
( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)( 40, 41)
( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)( 56, 69)
( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 75,111)( 76,113)
( 77,112)( 78,114)( 79,115)( 80,117)( 81,116)( 82,118)( 83,119)( 84,121)
( 85,120)( 86,122)( 87,135)( 88,137)( 89,136)( 90,138)( 91,139)( 92,141)
( 93,140)( 94,142)( 95,143)( 96,145)( 97,144)( 98,146)( 99,123)(100,125)
(101,124)(102,126)(103,127)(104,129)(105,128)(106,130)(107,131)(108,133)
(109,132)(110,134);;
s3 := ( 3, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 23)( 8, 24)( 9, 26)( 10, 25)
( 11, 19)( 12, 20)( 13, 22)( 14, 21)( 29, 30)( 31, 35)( 32, 36)( 33, 38)
( 34, 37)( 39, 51)( 40, 52)( 41, 54)( 42, 53)( 43, 59)( 44, 60)( 45, 62)
( 46, 61)( 47, 55)( 48, 56)( 49, 58)( 50, 57)( 65, 66)( 67, 71)( 68, 72)
( 69, 74)( 70, 73)( 75, 87)( 76, 88)( 77, 90)( 78, 89)( 79, 95)( 80, 96)
( 81, 98)( 82, 97)( 83, 91)( 84, 92)( 85, 94)( 86, 93)(101,102)(103,107)
(104,108)(105,110)(106,109)(111,123)(112,124)(113,126)(114,125)(115,131)
(116,132)(117,134)(118,133)(119,127)(120,128)(121,130)(122,129)(137,138)
(139,143)(140,144)(141,146)(142,145);;
s4 := ( 3, 10)( 4, 8)( 5, 9)( 6, 7)( 11, 14)( 15, 34)( 16, 32)( 17, 33)
( 18, 31)( 19, 30)( 20, 28)( 21, 29)( 22, 27)( 23, 38)( 24, 36)( 25, 37)
( 26, 35)( 39, 46)( 40, 44)( 41, 45)( 42, 43)( 47, 50)( 51, 70)( 52, 68)
( 53, 69)( 54, 67)( 55, 66)( 56, 64)( 57, 65)( 58, 63)( 59, 74)( 60, 72)
( 61, 73)( 62, 71)( 75, 82)( 76, 80)( 77, 81)( 78, 79)( 83, 86)( 87,106)
( 88,104)( 89,105)( 90,103)( 91,102)( 92,100)( 93,101)( 94, 99)( 95,110)
( 96,108)( 97,109)( 98,107)(111,118)(112,116)(113,117)(114,115)(119,122)
(123,142)(124,140)(125,141)(126,139)(127,138)(128,136)(129,137)(130,135)
(131,146)(132,144)(133,145)(134,143);;
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,
s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(146)!(1,2);
s1 := Sym(146)!( 3, 75)( 4, 76)( 5, 77)( 6, 78)( 7, 79)( 8, 80)( 9, 81)
( 10, 82)( 11, 83)( 12, 84)( 13, 85)( 14, 86)( 15, 87)( 16, 88)( 17, 89)
( 18, 90)( 19, 91)( 20, 92)( 21, 93)( 22, 94)( 23, 95)( 24, 96)( 25, 97)
( 26, 98)( 27, 99)( 28,100)( 29,101)( 30,102)( 31,103)( 32,104)( 33,105)
( 34,106)( 35,107)( 36,108)( 37,109)( 38,110)( 39,111)( 40,112)( 41,113)
( 42,114)( 43,115)( 44,116)( 45,117)( 46,118)( 47,119)( 48,120)( 49,121)
( 50,122)( 51,123)( 52,124)( 53,125)( 54,126)( 55,127)( 56,128)( 57,129)
( 58,130)( 59,131)( 60,132)( 61,133)( 62,134)( 63,135)( 64,136)( 65,137)
( 66,138)( 67,139)( 68,140)( 69,141)( 70,142)( 71,143)( 72,144)( 73,145)
( 74,146);
s2 := Sym(146)!( 4, 5)( 8, 9)( 12, 13)( 15, 27)( 16, 29)( 17, 28)( 18, 30)
( 19, 31)( 20, 33)( 21, 32)( 22, 34)( 23, 35)( 24, 37)( 25, 36)( 26, 38)
( 40, 41)( 44, 45)( 48, 49)( 51, 63)( 52, 65)( 53, 64)( 54, 66)( 55, 67)
( 56, 69)( 57, 68)( 58, 70)( 59, 71)( 60, 73)( 61, 72)( 62, 74)( 75,111)
( 76,113)( 77,112)( 78,114)( 79,115)( 80,117)( 81,116)( 82,118)( 83,119)
( 84,121)( 85,120)( 86,122)( 87,135)( 88,137)( 89,136)( 90,138)( 91,139)
( 92,141)( 93,140)( 94,142)( 95,143)( 96,145)( 97,144)( 98,146)( 99,123)
(100,125)(101,124)(102,126)(103,127)(104,129)(105,128)(106,130)(107,131)
(108,133)(109,132)(110,134);
s3 := Sym(146)!( 3, 15)( 4, 16)( 5, 18)( 6, 17)( 7, 23)( 8, 24)( 9, 26)
( 10, 25)( 11, 19)( 12, 20)( 13, 22)( 14, 21)( 29, 30)( 31, 35)( 32, 36)
( 33, 38)( 34, 37)( 39, 51)( 40, 52)( 41, 54)( 42, 53)( 43, 59)( 44, 60)
( 45, 62)( 46, 61)( 47, 55)( 48, 56)( 49, 58)( 50, 57)( 65, 66)( 67, 71)
( 68, 72)( 69, 74)( 70, 73)( 75, 87)( 76, 88)( 77, 90)( 78, 89)( 79, 95)
( 80, 96)( 81, 98)( 82, 97)( 83, 91)( 84, 92)( 85, 94)( 86, 93)(101,102)
(103,107)(104,108)(105,110)(106,109)(111,123)(112,124)(113,126)(114,125)
(115,131)(116,132)(117,134)(118,133)(119,127)(120,128)(121,130)(122,129)
(137,138)(139,143)(140,144)(141,146)(142,145);
s4 := Sym(146)!( 3, 10)( 4, 8)( 5, 9)( 6, 7)( 11, 14)( 15, 34)( 16, 32)
( 17, 33)( 18, 31)( 19, 30)( 20, 28)( 21, 29)( 22, 27)( 23, 38)( 24, 36)
( 25, 37)( 26, 35)( 39, 46)( 40, 44)( 41, 45)( 42, 43)( 47, 50)( 51, 70)
( 52, 68)( 53, 69)( 54, 67)( 55, 66)( 56, 64)( 57, 65)( 58, 63)( 59, 74)
( 60, 72)( 61, 73)( 62, 71)( 75, 82)( 76, 80)( 77, 81)( 78, 79)( 83, 86)
( 87,106)( 88,104)( 89,105)( 90,103)( 91,102)( 92,100)( 93,101)( 94, 99)
( 95,110)( 96,108)( 97,109)( 98,107)(111,118)(112,116)(113,117)(114,115)
(119,122)(123,142)(124,140)(125,141)(126,139)(127,138)(128,136)(129,137)
(130,135)(131,146)(132,144)(133,145)(134,143);
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, s3*s4*s3*s4*s3*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3 >;
to this polytope