Overview
- Group
- SmallGroup(1728,12317)
- Rank
- 3
- Schläfli Type
- {24,3}
- Vertices, edges, …
- 288, 432, 36
- Order of s0s1s2
- 6
- Order of s0s1s2s1
- 24
- Also known as
- {24,3}6. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
3-fold
4-fold
9-fold
12-fold
16-fold
36-fold
48-fold
72-fold
144-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*s0*s2*(s1*s0)^5*s1*s2*s1> of order 2
18 facets
- 18 of {24}*48
144 vertex figures
- 144 of {3}*6
P/N, where N=<(s0*s1)^12, s0*s1*s2*(s1*s0)^7*s2*(s1*s0)^4*s1*s2> of order 4
12 facets
72 vertex figures
- 72 of {3}*6
P/N, where N=<s0*s1*s0*s2*(s1*s0)^5*s1*s2*s1, (s0*s1)^12> of order 4
12 facets
72 vertex figures
- 72 of {3}*6
P/N, where N=<(s0*s1)^8, s0*s1*s0*s2*(s1*s0)^5*s1*s2*s1> of order 6
10 facets
48 vertex figures
- 48 of {3}*6
P/N, where N=<(s0*s1)^4, s0*s1*s2*(s1*s0)^11*s1*s2*s1> of order 12
8 facets
24 vertex figures
- 24 of {3}*6
P/N, where N=<(s0*s1)^4, s1*s2*(s1*s0)^3*s2*(s1*s0)^2*s1*s2> of order 12
8 facets
24 vertex figures
- 24 of {3}*6
Representations
Permutation Representation (GAP)
s0 := ( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 14)( 6, 13)( 7, 16)( 8, 15)( 17, 41)( 18, 42)( 19, 43)( 20, 44)( 21, 46)( 22, 45)( 23, 48)( 24, 47)( 25, 33)( 26, 34)( 27, 35)( 28, 36)( 29, 38)( 30, 37)( 31, 40)( 32, 39)( 49,105)( 50,106)( 51,107)( 52,108)( 53,110)( 54,109)( 55,112)( 56,111)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61,102)( 62,101)( 63,104)( 64,103)( 65,137)( 66,138)( 67,139)( 68,140)( 69,142)( 70,141)( 71,144)( 72,143)( 73,129)( 74,130)( 75,131)( 76,132)( 77,134)( 78,133)( 79,136)( 80,135)( 81,121)( 82,122)( 83,123)( 84,124)( 85,126)( 86,125)( 87,128)( 88,127)( 89,113)( 90,114)( 91,115)( 92,116)( 93,118)( 94,117)( 95,120)( 96,119);; s1 := ( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 53)( 6, 54)( 7, 56)( 8, 55)( 9, 63)( 10, 64)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 57)( 16, 58)( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 79)( 26, 80)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 73)( 32, 74)( 33, 81)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 86)( 39, 88)( 40, 87)( 41, 95)( 42, 96)( 43, 94)( 44, 93)( 45, 92)( 46, 91)( 47, 89)( 48, 90)( 99,100)(103,104)(105,111)(106,112)(107,110)(108,109)(115,116)(119,120)(121,127)(122,128)(123,126)(124,125)(131,132)(135,136)(137,143)(138,144)(139,142)(140,141);; s2 := ( 1, 9)( 2, 12)( 3, 11)( 4, 10)( 5, 7)( 14, 16)( 17, 25)( 18, 28)( 19, 27)( 20, 26)( 21, 23)( 30, 32)( 33, 41)( 34, 44)( 35, 43)( 36, 42)( 37, 39)( 46, 48)( 49,137)( 50,140)( 51,139)( 52,138)( 53,135)( 54,134)( 55,133)( 56,136)( 57,129)( 58,132)( 59,131)( 60,130)( 61,141)( 62,144)( 63,143)( 64,142)( 65,105)( 66,108)( 67,107)( 68,106)( 69,103)( 70,102)( 71,101)( 72,104)( 73, 97)( 74,100)( 75, 99)( 76, 98)( 77,109)( 78,112)( 79,111)( 80,110)( 81,121)( 82,124)( 83,123)( 84,122)( 85,119)( 86,118)( 87,117)( 88,120)( 89,113)( 90,116)( 91,115)( 92,114)( 93,125)( 94,128)( 95,127)( 96,126);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2,
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 1, 9)( 2, 10)( 3, 11)( 4, 12)( 5, 14)( 6, 13)( 7, 16)( 8, 15)( 17, 41)( 18, 42)( 19, 43)( 20, 44)( 21, 46)( 22, 45)( 23, 48)( 24, 47)( 25, 33)( 26, 34)( 27, 35)( 28, 36)( 29, 38)( 30, 37)( 31, 40)( 32, 39)( 49,105)( 50,106)( 51,107)( 52,108)( 53,110)( 54,109)( 55,112)( 56,111)( 57, 97)( 58, 98)( 59, 99)( 60,100)( 61,102)( 62,101)( 63,104)( 64,103)( 65,137)( 66,138)( 67,139)( 68,140)( 69,142)( 70,141)( 71,144)( 72,143)( 73,129)( 74,130)( 75,131)( 76,132)( 77,134)( 78,133)( 79,136)( 80,135)( 81,121)( 82,122)( 83,123)( 84,124)( 85,126)( 86,125)( 87,128)( 88,127)( 89,113)( 90,114)( 91,115)( 92,116)( 93,118)( 94,117)( 95,120)( 96,119); s1 := Sym(144)!( 1, 49)( 2, 50)( 3, 52)( 4, 51)( 5, 53)( 6, 54)( 7, 56)( 8, 55)( 9, 63)( 10, 64)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 57)( 16, 58)( 17, 65)( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 79)( 26, 80)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 73)( 32, 74)( 33, 81)( 34, 82)( 35, 84)( 36, 83)( 37, 85)( 38, 86)( 39, 88)( 40, 87)( 41, 95)( 42, 96)( 43, 94)( 44, 93)( 45, 92)( 46, 91)( 47, 89)( 48, 90)( 99,100)(103,104)(105,111)(106,112)(107,110)(108,109)(115,116)(119,120)(121,127)(122,128)(123,126)(124,125)(131,132)(135,136)(137,143)(138,144)(139,142)(140,141); s2 := Sym(144)!( 1, 9)( 2, 12)( 3, 11)( 4, 10)( 5, 7)( 14, 16)( 17, 25)( 18, 28)( 19, 27)( 20, 26)( 21, 23)( 30, 32)( 33, 41)( 34, 44)( 35, 43)( 36, 42)( 37, 39)( 46, 48)( 49,137)( 50,140)( 51,139)( 52,138)( 53,135)( 54,134)( 55,133)( 56,136)( 57,129)( 58,132)( 59,131)( 60,130)( 61,141)( 62,144)( 63,143)( 64,142)( 65,105)( 66,108)( 67,107)( 68,106)( 69,103)( 70,102)( 71,101)( 72,104)( 73, 97)( 74,100)( 75, 99)( 76, 98)( 77,109)( 78,112)( 79,111)( 80,110)( 81,121)( 82,124)( 83,123)( 84,122)( 85,119)( 86,118)( 87,117)( 88,120)( 89,113)( 90,116)( 91,115)( 92,114)( 93,125)( 94,128)( 95,127)( 96,126); poly := sub<Sym(144)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References
None.
to this polytope.