Overview
- Group
- SmallGroup(1728,12249)
- Rank
- 3
- Schläfli Type
- {9,6}
- Vertices, edges, …
- 144, 432, 96
- Order of s0s1s2
- 72
- Order of s0s1s2s1
- 6
- Also known as
- if this polytope has a 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=<s1*(s0*(s2*s1)^2)^2*s0*(s2*s1)^2*s0*s2*s1*s2> of order 2
48 facets
- 48 of {9}*18
72 vertex figures
- 72 of {6}*12
P/N, where N=<s1*(s2*s1*s0)^2*(s2*s1)^2*s0*(s1*s2)^2*s1*s0*(s1*s2)^2> of order 3
32 facets
- 32 of {9}*18
54 vertex figures
P/N, where N=<s0*s1*(s2*s1*s0)^2*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 4
24 facets
- 24 of {9}*18
36 vertex figures
- 36 of {6}*12
P/N, where N=<s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 4
24 facets
- 24 of {9}*18
36 vertex figures
- 36 of {6}*12
P/N, where N=<s1*s2*s1*(s0*(s2*s1)^2)^2*s0*(s2*s1)^2*s2> of order 4
24 facets
- 24 of {9}*18
36 vertex figures
- 36 of {6}*12
P/N, where N=<s0*s1*(s2*s1*s0)^2*(s2*s1)^2*s0*(s1*s2)^3> of order 4
24 facets
- 24 of {9}*18
36 vertex figures
- 36 of {6}*12
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 7, 8)( 9, 15)( 10, 16)( 11, 14)( 12, 13)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 47)( 26, 48)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 41)( 32, 42)( 49,129)( 50,130)( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,143)( 58,144)( 59,142)( 60,141)( 61,140)( 62,139)( 63,137)( 64,138)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,127)( 74,128)( 75,126)( 76,125)( 77,124)( 78,123)( 79,121)( 80,122)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,111)( 90,112)( 91,110)( 92,109)( 93,108)( 94,107)( 95,105)( 96,106);; s1 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 61)( 6, 64)( 7, 63)( 8, 62)( 9, 59)( 10, 58)( 11, 57)( 12, 60)( 13, 53)( 14, 56)( 15, 55)( 16, 54)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 91)( 26, 90)( 27, 89)( 28, 92)( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 77)( 38, 80)( 39, 79)( 40, 78)( 41, 75)( 42, 74)( 43, 73)( 44, 76)( 45, 69)( 46, 72)( 47, 71)( 48, 70)( 97,129)( 98,132)( 99,131)(100,130)(101,141)(102,144)(103,143)(104,142)(105,139)(106,138)(107,137)(108,140)(109,133)(110,136)(111,135)(112,134)(114,116)(117,125)(118,128)(119,127)(120,126)(121,123);; s2 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 13, 14)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 30)( 33, 37)( 34, 38)( 35, 40)( 36, 39)( 43, 44)( 45, 46)( 49, 53)( 50, 54)( 51, 56)( 52, 55)( 59, 60)( 61, 62)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 75, 76)( 77, 78)( 81, 85)( 82, 86)( 83, 88)( 84, 87)( 91, 92)( 93, 94)( 97,101)( 98,102)( 99,104)(100,103)(107,108)(109,110)(113,117)(114,118)(115,120)(116,119)(123,124)(125,126)(129,133)(130,134)(131,136)(132,135)(139,140)(141,142);; 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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(144)!( 3, 4)( 7, 8)( 9, 15)( 10, 16)( 11, 14)( 12, 13)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 47)( 26, 48)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 41)( 32, 42)( 49,129)( 50,130)( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,143)( 58,144)( 59,142)( 60,141)( 61,140)( 62,139)( 63,137)( 64,138)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,127)( 74,128)( 75,126)( 76,125)( 77,124)( 78,123)( 79,121)( 80,122)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,111)( 90,112)( 91,110)( 92,109)( 93,108)( 94,107)( 95,105)( 96,106); s1 := Sym(144)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 61)( 6, 64)( 7, 63)( 8, 62)( 9, 59)( 10, 58)( 11, 57)( 12, 60)( 13, 53)( 14, 56)( 15, 55)( 16, 54)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 91)( 26, 90)( 27, 89)( 28, 92)( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 77)( 38, 80)( 39, 79)( 40, 78)( 41, 75)( 42, 74)( 43, 73)( 44, 76)( 45, 69)( 46, 72)( 47, 71)( 48, 70)( 97,129)( 98,132)( 99,131)(100,130)(101,141)(102,144)(103,143)(104,142)(105,139)(106,138)(107,137)(108,140)(109,133)(110,136)(111,135)(112,134)(114,116)(117,125)(118,128)(119,127)(120,126)(121,123); s2 := Sym(144)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)( 11, 12)( 13, 14)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 27, 28)( 29, 30)( 33, 37)( 34, 38)( 35, 40)( 36, 39)( 43, 44)( 45, 46)( 49, 53)( 50, 54)( 51, 56)( 52, 55)( 59, 60)( 61, 62)( 65, 69)( 66, 70)( 67, 72)( 68, 71)( 75, 76)( 77, 78)( 81, 85)( 82, 86)( 83, 88)( 84, 87)( 91, 92)( 93, 94)( 97,101)( 98,102)( 99,104)(100,103)(107,108)(109,110)(113,117)(114,118)(115,120)(116,119)(123,124)(125,126)(129,133)(130,134)(131,136)(132,135)(139,140)(141,142); 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*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References
None.
to this polytope.