Overview
- Group
- SmallGroup(1728,46119)
- Rank
- 4
- Schläfli Type
- {4,3,12}
- Vertices, edges, …
- 4, 36, 108, 72
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{4,3}3,{3,12}6}. if this polytope has another name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
4-fold
9-fold
12-fold
18-fold
36-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<s1*s2*s1*(s3*s2)^5*s1*s3*s2*s3> of order 2
36 facets
- 36 of {4,3}*24
4 vertex figures
- 4 of 2-fold non-regular quotient of {3,12}*432
P/N, where N=<s1*s2*s1*(s3*s2)^5*s1*s3*s2> of order 2
36 facets
- 36 of {4,3}*24
4 vertex figures
- 4 of 2-fold non-regular quotient of {3,12}*432
P/N, where N=<s1*s2*s1*(s3*s2)^3*s1*s3*s2> of order 3
24 facets
- 24 of {4,3}*24
4 vertex figures
- 4 of 3-fold non-regular quotient of {3,12}*432
P/N, where N=<s1*(s2*s1*s3)^2*s2*s3, (s1*s3*s2)^3> of order 6
12 facets
- 12 of {4,3}*24
4 vertex figures
- 4 of 6-fold non-regular quotient of {3,12}*432
P/N, where N=<s1*(s2*s1*s3)^2*s2> of order 6
12 facets
- 12 of {4,3}*24
4 vertex figures
- 4 of 6-fold non-regular quotient of {3,12}*432
P/N, where N=<s1*(s2*s3)^3*s2*s1*s3, s2*s1*(s3*s2)^2*s1*(s3*s2)^3*s3> of order 6
12 facets
- 12 of {4,3}*24
4 vertex figures
- 4 of 6-fold non-regular quotient of {3,12}*432
Representations
Permutation Representation (GAP)
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144);; s1 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)( 23, 24)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81,129)( 82,130)( 83,132)( 84,131)( 85,133)( 86,134)( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)( 94,138)( 95,140)( 96,139);; s2 := ( 1,113)( 2,116)( 3,115)( 4,114)( 5,125)( 6,128)( 7,127)( 8,126)( 9,121)( 10,124)( 11,123)( 12,122)( 13,117)( 14,120)( 15,119)( 16,118)( 17,129)( 18,132)( 19,131)( 20,130)( 21,141)( 22,144)( 23,143)( 24,142)( 25,137)( 26,140)( 27,139)( 28,138)( 29,133)( 30,136)( 31,135)( 32,134)( 33, 97)( 34,100)( 35, 99)( 36, 98)( 37,109)( 38,112)( 39,111)( 40,110)( 41,105)( 42,108)( 43,107)( 44,106)( 45,101)( 46,104)( 47,103)( 48,102)( 50, 52)( 53, 61)( 54, 64)( 55, 63)( 56, 62)( 58, 60)( 66, 68)( 69, 77)( 70, 80)( 71, 79)( 72, 78)( 74, 76)( 82, 84)( 85, 93)( 86, 96)( 87, 95)( 88, 94)( 90, 92);; s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 34)( 18, 33)( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 40)( 24, 39)( 25, 42)( 26, 41)( 27, 44)( 28, 43)( 29, 46)( 30, 45)( 31, 48)( 32, 47)( 49, 98)( 50, 97)( 51,100)( 52, 99)( 53,102)( 54,101)( 55,104)( 56,103)( 57,106)( 58,105)( 59,108)( 60,107)( 61,110)( 62,109)( 63,112)( 64,111)( 65,130)( 66,129)( 67,132)( 68,131)( 69,134)( 70,133)( 71,136)( 72,135)( 73,138)( 74,137)( 75,140)( 76,139)( 77,142)( 78,141)( 79,144)( 80,143)( 81,114)( 82,113)( 83,116)( 84,115)( 85,118)( 86,117)( 87,120)( 88,119)( 89,122)( 90,121)( 91,124)( 92,123)( 93,126)( 94,125)( 95,128)( 96,127);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 13)( 6, 14)( 7, 15)( 8, 16)( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 49, 57)( 50, 58)( 51, 59)( 52, 60)( 53, 61)( 54, 62)( 55, 63)( 56, 64)( 65, 73)( 66, 74)( 67, 75)( 68, 76)( 69, 77)( 70, 78)( 71, 79)( 72, 80)( 81, 89)( 82, 90)( 83, 91)( 84, 92)( 85, 93)( 86, 94)( 87, 95)( 88, 96)( 97,105)( 98,106)( 99,107)(100,108)(101,109)(102,110)(103,111)(104,112)(113,121)(114,122)(115,123)(116,124)(117,125)(118,126)(119,127)(120,128)(129,137)(130,138)(131,139)(132,140)(133,141)(134,142)(135,143)(136,144); s1 := Sym(144)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 19, 20)( 23, 24)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 35, 36)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 97)( 50, 98)( 51,100)( 52, 99)( 53,101)( 54,102)( 55,104)( 56,103)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81,129)( 82,130)( 83,132)( 84,131)( 85,133)( 86,134)( 87,136)( 88,135)( 89,141)( 90,142)( 91,144)( 92,143)( 93,137)( 94,138)( 95,140)( 96,139); s2 := Sym(144)!( 1,113)( 2,116)( 3,115)( 4,114)( 5,125)( 6,128)( 7,127)( 8,126)( 9,121)( 10,124)( 11,123)( 12,122)( 13,117)( 14,120)( 15,119)( 16,118)( 17,129)( 18,132)( 19,131)( 20,130)( 21,141)( 22,144)( 23,143)( 24,142)( 25,137)( 26,140)( 27,139)( 28,138)( 29,133)( 30,136)( 31,135)( 32,134)( 33, 97)( 34,100)( 35, 99)( 36, 98)( 37,109)( 38,112)( 39,111)( 40,110)( 41,105)( 42,108)( 43,107)( 44,106)( 45,101)( 46,104)( 47,103)( 48,102)( 50, 52)( 53, 61)( 54, 64)( 55, 63)( 56, 62)( 58, 60)( 66, 68)( 69, 77)( 70, 80)( 71, 79)( 72, 78)( 74, 76)( 82, 84)( 85, 93)( 86, 96)( 87, 95)( 88, 94)( 90, 92); s3 := Sym(144)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 34)( 18, 33)( 19, 36)( 20, 35)( 21, 38)( 22, 37)( 23, 40)( 24, 39)( 25, 42)( 26, 41)( 27, 44)( 28, 43)( 29, 46)( 30, 45)( 31, 48)( 32, 47)( 49, 98)( 50, 97)( 51,100)( 52, 99)( 53,102)( 54,101)( 55,104)( 56,103)( 57,106)( 58,105)( 59,108)( 60,107)( 61,110)( 62,109)( 63,112)( 64,111)( 65,130)( 66,129)( 67,132)( 68,131)( 69,134)( 70,133)( 71,136)( 72,135)( 73,138)( 74,137)( 75,140)( 76,139)( 77,142)( 78,141)( 79,144)( 80,143)( 81,114)( 82,113)( 83,116)( 84,115)( 85,118)( 86,117)( 87,120)( 88,119)( 89,122)( 90,121)( 91,124)( 92,123)( 93,126)( 94,125)( 95,128)( 96,127); poly := sub<Sym(144)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*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 >;
References
None.
to this polytope.