Overview
- Group
- SmallGroup(1728,46100)
- Rank
- 4
- Schläfli Type
- {4,6,9}
- Vertices, edges, …
- 16, 48, 108, 9
- Order of s0s1s2s3
- 18
- Order of s0s1s2s3s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-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=<s0*s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 2
9 facets
- 6 of 2-fold non-regular quotient of {4,6}*192a
- 3 of 2-fold non-regular quotient of {4,6}*192a
8 vertex figures
- 8 of {6,9}*108
P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4
9 facets
- 6 of 4-fold non-regular quotient of {4,6}*192a
- 3 of {4,6}*48c
4 vertex figures
- 4 of {6,9}*108
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2> of order 4
9 facets
- 9 of 4-fold non-regular quotient of {4,6}*192a
4 vertex figures
- 4 of {6,9}*108
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 := ( 2, 5)( 3, 13)( 4, 9)( 7, 14)( 8, 10)( 11, 16)( 18, 21)( 19, 29)( 20, 25)( 23, 30)( 24, 26)( 27, 32)( 34, 37)( 35, 45)( 36, 41)( 39, 46)( 40, 42)( 43, 48)( 50, 53)( 51, 61)( 52, 57)( 55, 62)( 56, 58)( 59, 64)( 66, 69)( 67, 77)( 68, 73)( 71, 78)( 72, 74)( 75, 80)( 82, 85)( 83, 93)( 84, 89)( 87, 94)( 88, 90)( 91, 96)( 98,101)( 99,109)(100,105)(103,110)(104,106)(107,112)(114,117)(115,125)(116,121)(119,126)(120,122)(123,128)(130,133)(131,141)(132,137)(135,142)(136,138)(139,144);; s2 := ( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 61)( 6, 62)( 7, 64)( 8, 63)( 9, 57)( 10, 58)( 11, 60)( 12, 59)( 13, 53)( 14, 54)( 15, 56)( 16, 55)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 93)( 22, 94)( 23, 96)( 24, 95)( 25, 89)( 26, 90)( 27, 92)( 28, 91)( 29, 85)( 30, 86)( 31, 88)( 32, 87)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)( 40, 79)( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)( 48, 71)( 97,129)( 98,130)( 99,132)(100,131)(101,141)(102,142)(103,144)(104,143)(105,137)(106,138)(107,140)(108,139)(109,133)(110,134)(111,136)(112,135)(115,116)(117,125)(118,126)(119,128)(120,127)(123,124);; s3 := ( 1, 97)( 2, 99)( 3, 98)( 4,100)( 5,109)( 6,111)( 7,110)( 8,112)( 9,105)( 10,107)( 11,106)( 12,108)( 13,101)( 14,103)( 15,102)( 16,104)( 17,129)( 18,131)( 19,130)( 20,132)( 21,141)( 22,143)( 23,142)( 24,144)( 25,137)( 26,139)( 27,138)( 28,140)( 29,133)( 30,135)( 31,134)( 32,136)( 33,113)( 34,115)( 35,114)( 36,116)( 37,125)( 38,127)( 39,126)( 40,128)( 41,121)( 42,123)( 43,122)( 44,124)( 45,117)( 46,119)( 47,118)( 48,120)( 50, 51)( 53, 61)( 54, 63)( 55, 62)( 56, 64)( 58, 59)( 65, 81)( 66, 83)( 67, 82)( 68, 84)( 69, 93)( 70, 95)( 71, 94)( 72, 96)( 73, 89)( 74, 91)( 75, 90)( 76, 92)( 77, 85)( 78, 87)( 79, 86)( 80, 88);; 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, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s3*s2*s1*s0*s1*s2*s1*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)!( 2, 5)( 3, 13)( 4, 9)( 7, 14)( 8, 10)( 11, 16)( 18, 21)( 19, 29)( 20, 25)( 23, 30)( 24, 26)( 27, 32)( 34, 37)( 35, 45)( 36, 41)( 39, 46)( 40, 42)( 43, 48)( 50, 53)( 51, 61)( 52, 57)( 55, 62)( 56, 58)( 59, 64)( 66, 69)( 67, 77)( 68, 73)( 71, 78)( 72, 74)( 75, 80)( 82, 85)( 83, 93)( 84, 89)( 87, 94)( 88, 90)( 91, 96)( 98,101)( 99,109)(100,105)(103,110)(104,106)(107,112)(114,117)(115,125)(116,121)(119,126)(120,122)(123,128)(130,133)(131,141)(132,137)(135,142)(136,138)(139,144); s2 := Sym(144)!( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 61)( 6, 62)( 7, 64)( 8, 63)( 9, 57)( 10, 58)( 11, 60)( 12, 59)( 13, 53)( 14, 54)( 15, 56)( 16, 55)( 17, 81)( 18, 82)( 19, 84)( 20, 83)( 21, 93)( 22, 94)( 23, 96)( 24, 95)( 25, 89)( 26, 90)( 27, 92)( 28, 91)( 29, 85)( 30, 86)( 31, 88)( 32, 87)( 33, 65)( 34, 66)( 35, 68)( 36, 67)( 37, 77)( 38, 78)( 39, 80)( 40, 79)( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)( 48, 71)( 97,129)( 98,130)( 99,132)(100,131)(101,141)(102,142)(103,144)(104,143)(105,137)(106,138)(107,140)(108,139)(109,133)(110,134)(111,136)(112,135)(115,116)(117,125)(118,126)(119,128)(120,127)(123,124); s3 := Sym(144)!( 1, 97)( 2, 99)( 3, 98)( 4,100)( 5,109)( 6,111)( 7,110)( 8,112)( 9,105)( 10,107)( 11,106)( 12,108)( 13,101)( 14,103)( 15,102)( 16,104)( 17,129)( 18,131)( 19,130)( 20,132)( 21,141)( 22,143)( 23,142)( 24,144)( 25,137)( 26,139)( 27,138)( 28,140)( 29,133)( 30,135)( 31,134)( 32,136)( 33,113)( 34,115)( 35,114)( 36,116)( 37,125)( 38,127)( 39,126)( 40,128)( 41,121)( 42,123)( 43,122)( 44,124)( 45,117)( 46,119)( 47,118)( 48,120)( 50, 51)( 53, 61)( 54, 63)( 55, 62)( 56, 64)( 58, 59)( 65, 81)( 66, 83)( 67, 82)( 68, 84)( 69, 93)( 70, 95)( 71, 94)( 72, 96)( 73, 89)( 74, 91)( 75, 90)( 76, 92)( 77, 85)( 78, 87)( 79, 86)( 80, 88); 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, s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s3*s2*s1*s0*s1*s2*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References
None.
to this polytope.