Overview
- Group
- SmallGroup(576,2279)
- Rank
- 3
- Schläfli Type
- {24,12}
- Vertices, edges, …
- 24, 144, 12
- Order of s0s1s2
- 24
- Order of s0s1s2s1
- 12
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
- Self-Petrie
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
9-fold
12-fold
16-fold
18-fold
24-fold
36-fold
48-fold
72-fold
Covers minimal covers in bold
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 19, 28)( 20, 30)( 21, 29)( 22, 31)( 23, 33)( 24, 32)( 25, 34)( 26, 36)( 27, 35)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 50, 51)( 53, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 67)( 59, 69)( 60, 68)( 61, 70)( 62, 72)( 63, 71)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)( 78, 95)( 79, 97)( 80, 99)( 81, 98)( 82,100)( 83,102)( 84,101)( 85,103)( 86,105)( 87,104)( 88,106)( 89,108)( 90,107)(109,127)(110,129)(111,128)(112,130)(113,132)(114,131)(115,133)(116,135)(117,134)(118,136)(119,138)(120,137)(121,139)(122,141)(123,140)(124,142)(125,144)(126,143);; s1 := ( 1, 74)( 2, 73)( 3, 75)( 4, 80)( 5, 79)( 6, 81)( 7, 77)( 8, 76)( 9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)( 16, 86)( 17, 85)( 18, 87)( 19,101)( 20,100)( 21,102)( 22,107)( 23,106)( 24,108)( 25,104)( 26,103)( 27,105)( 28, 92)( 29, 91)( 30, 93)( 31, 98)( 32, 97)( 33, 99)( 34, 95)( 35, 94)( 36, 96)( 37,119)( 38,118)( 39,120)( 40,125)( 41,124)( 42,126)( 43,122)( 44,121)( 45,123)( 46,110)( 47,109)( 48,111)( 49,116)( 50,115)( 51,117)( 52,113)( 53,112)( 54,114)( 55,128)( 56,127)( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,137)( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141);; s2 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 34)( 26, 36)( 27, 35)( 37, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 43, 52)( 44, 54)( 45, 53)( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 67)( 65, 69)( 66, 68)( 71, 72)( 73,130)( 74,132)( 75,131)( 76,127)( 77,129)( 78,128)( 79,133)( 80,135)( 81,134)( 82,139)( 83,141)( 84,140)( 85,136)( 86,138)( 87,137)( 88,142)( 89,144)( 90,143)( 91,112)( 92,114)( 93,113)( 94,109)( 95,111)( 96,110)( 97,115)( 98,117)( 99,116)(100,121)(101,123)(102,122)(103,118)(104,120)(105,119)(106,124)(107,126)(108,125);; 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, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 2, 3)( 5, 6)( 8, 9)( 11, 12)( 14, 15)( 17, 18)( 19, 28)( 20, 30)( 21, 29)( 22, 31)( 23, 33)( 24, 32)( 25, 34)( 26, 36)( 27, 35)( 38, 39)( 41, 42)( 44, 45)( 47, 48)( 50, 51)( 53, 54)( 55, 64)( 56, 66)( 57, 65)( 58, 67)( 59, 69)( 60, 68)( 61, 70)( 62, 72)( 63, 71)( 73, 91)( 74, 93)( 75, 92)( 76, 94)( 77, 96)( 78, 95)( 79, 97)( 80, 99)( 81, 98)( 82,100)( 83,102)( 84,101)( 85,103)( 86,105)( 87,104)( 88,106)( 89,108)( 90,107)(109,127)(110,129)(111,128)(112,130)(113,132)(114,131)(115,133)(116,135)(117,134)(118,136)(119,138)(120,137)(121,139)(122,141)(123,140)(124,142)(125,144)(126,143); s1 := Sym(144)!( 1, 74)( 2, 73)( 3, 75)( 4, 80)( 5, 79)( 6, 81)( 7, 77)( 8, 76)( 9, 78)( 10, 83)( 11, 82)( 12, 84)( 13, 89)( 14, 88)( 15, 90)( 16, 86)( 17, 85)( 18, 87)( 19,101)( 20,100)( 21,102)( 22,107)( 23,106)( 24,108)( 25,104)( 26,103)( 27,105)( 28, 92)( 29, 91)( 30, 93)( 31, 98)( 32, 97)( 33, 99)( 34, 95)( 35, 94)( 36, 96)( 37,119)( 38,118)( 39,120)( 40,125)( 41,124)( 42,126)( 43,122)( 44,121)( 45,123)( 46,110)( 47,109)( 48,111)( 49,116)( 50,115)( 51,117)( 52,113)( 53,112)( 54,114)( 55,128)( 56,127)( 57,129)( 58,134)( 59,133)( 60,135)( 61,131)( 62,130)( 63,132)( 64,137)( 65,136)( 66,138)( 67,143)( 68,142)( 69,144)( 70,140)( 71,139)( 72,141); s2 := Sym(144)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 34)( 26, 36)( 27, 35)( 37, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 43, 52)( 44, 54)( 45, 53)( 55, 58)( 56, 60)( 57, 59)( 62, 63)( 64, 67)( 65, 69)( 66, 68)( 71, 72)( 73,130)( 74,132)( 75,131)( 76,127)( 77,129)( 78,128)( 79,133)( 80,135)( 81,134)( 82,139)( 83,141)( 84,140)( 85,136)( 86,138)( 87,137)( 88,142)( 89,144)( 90,143)( 91,112)( 92,114)( 93,113)( 94,109)( 95,111)( 96,110)( 97,115)( 98,117)( 99,116)(100,121)(101,123)(102,122)(103,118)(104,120)(105,119)(106,124)(107,126)(108,125); 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, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.