Overview
- Group
- SmallGroup(1152,32532)
- Rank
- 3
- Schläfli Type
- {36,4}
- Vertices, edges, …
- 144, 288, 16
- Order of s0s1s2
- 72
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
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
32-fold
36-fold
48-fold
72-fold
96-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)^2*(s2*s1*s0)^2*s1*s2*s1> of order 2
8 facets
- 8 of {36}*72
72 vertex figures
- 72 of {4}*8
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 2
8 facets
- 8 of {36}*72
72 vertex figures
- 72 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^2> of order 4
4 facets
- 4 of {36}*72
36 vertex figures
- 36 of {4}*8
P/N, where N=<(s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2*s2> of order 4
4 facets
- 4 of {36}*72
45 vertex figures
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2, (s0*s1)^18> of order 4
5 facets
36 vertex figures
- 36 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*s1*s0*s1*s2> of order 4
4 facets
- 4 of {36}*72
36 vertex figures
- 36 of {4}*8
Representations
Permutation Representation (GAP)
s0 := ( 1, 73)( 2, 75)( 3, 74)( 4, 81)( 5, 80)( 6, 79)( 7, 78)( 8, 77)( 9, 76)( 10, 82)( 11, 84)( 12, 83)( 13, 90)( 14, 89)( 15, 88)( 16, 87)( 17, 86)( 18, 85)( 19, 91)( 20, 93)( 21, 92)( 22, 99)( 23, 98)( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28,100)( 29,102)( 30,101)( 31,108)( 32,107)( 33,106)( 34,105)( 35,104)( 36,103)( 37,109)( 38,111)( 39,110)( 40,117)( 41,116)( 42,115)( 43,114)( 44,113)( 45,112)( 46,118)( 47,120)( 48,119)( 49,126)( 50,125)( 51,124)( 52,123)( 53,122)( 54,121)( 55,127)( 56,129)( 57,128)( 58,135)( 59,134)( 60,133)( 61,132)( 62,131)( 63,130)( 64,136)( 65,138)( 66,137)( 67,144)( 68,143)( 69,142)( 70,141)( 71,140)( 72,139);; s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 13)( 11, 15)( 12, 14)( 16, 18)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 36)( 26, 35)( 27, 34)( 37, 40)( 38, 42)( 39, 41)( 43, 45)( 46, 49)( 47, 51)( 48, 50)( 52, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 72)( 62, 71)( 63, 70)( 73,112)( 74,114)( 75,113)( 76,109)( 77,111)( 78,110)( 79,117)( 80,116)( 81,115)( 82,121)( 83,123)( 84,122)( 85,118)( 86,120)( 87,119)( 88,126)( 89,125)( 90,124)( 91,139)( 92,141)( 93,140)( 94,136)( 95,138)( 96,137)( 97,144)( 98,143)( 99,142)(100,130)(101,132)(102,131)(103,127)(104,129)(105,128)(106,135)(107,134)(108,133);; s2 := ( 37, 64)( 38, 65)( 39, 66)( 40, 67)( 41, 68)( 42, 69)( 43, 70)( 44, 71)( 45, 72)( 46, 55)( 47, 56)( 48, 57)( 49, 58)( 50, 59)( 51, 60)( 52, 61)( 53, 62)( 54, 63)(109,136)(110,137)(111,138)(112,139)(113,140)(114,141)(115,142)(116,143)(117,144)(118,127)(119,128)(120,129)(121,130)(122,131)(123,132)(124,133)(125,134)(126,135);; 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*s1*s2,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*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*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, 73)( 2, 75)( 3, 74)( 4, 81)( 5, 80)( 6, 79)( 7, 78)( 8, 77)( 9, 76)( 10, 82)( 11, 84)( 12, 83)( 13, 90)( 14, 89)( 15, 88)( 16, 87)( 17, 86)( 18, 85)( 19, 91)( 20, 93)( 21, 92)( 22, 99)( 23, 98)( 24, 97)( 25, 96)( 26, 95)( 27, 94)( 28,100)( 29,102)( 30,101)( 31,108)( 32,107)( 33,106)( 34,105)( 35,104)( 36,103)( 37,109)( 38,111)( 39,110)( 40,117)( 41,116)( 42,115)( 43,114)( 44,113)( 45,112)( 46,118)( 47,120)( 48,119)( 49,126)( 50,125)( 51,124)( 52,123)( 53,122)( 54,121)( 55,127)( 56,129)( 57,128)( 58,135)( 59,134)( 60,133)( 61,132)( 62,131)( 63,130)( 64,136)( 65,138)( 66,137)( 67,144)( 68,143)( 69,142)( 70,141)( 71,140)( 72,139); s1 := Sym(144)!( 1, 4)( 2, 6)( 3, 5)( 7, 9)( 10, 13)( 11, 15)( 12, 14)( 16, 18)( 19, 31)( 20, 33)( 21, 32)( 22, 28)( 23, 30)( 24, 29)( 25, 36)( 26, 35)( 27, 34)( 37, 40)( 38, 42)( 39, 41)( 43, 45)( 46, 49)( 47, 51)( 48, 50)( 52, 54)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 72)( 62, 71)( 63, 70)( 73,112)( 74,114)( 75,113)( 76,109)( 77,111)( 78,110)( 79,117)( 80,116)( 81,115)( 82,121)( 83,123)( 84,122)( 85,118)( 86,120)( 87,119)( 88,126)( 89,125)( 90,124)( 91,139)( 92,141)( 93,140)( 94,136)( 95,138)( 96,137)( 97,144)( 98,143)( 99,142)(100,130)(101,132)(102,131)(103,127)(104,129)(105,128)(106,135)(107,134)(108,133); s2 := Sym(144)!( 37, 64)( 38, 65)( 39, 66)( 40, 67)( 41, 68)( 42, 69)( 43, 70)( 44, 71)( 45, 72)( 46, 55)( 47, 56)( 48, 57)( 49, 58)( 50, 59)( 51, 60)( 52, 61)( 53, 62)( 54, 63)(109,136)(110,137)(111,138)(112,139)(113,140)(114,141)(115,142)(116,143)(117,144)(118,127)(119,128)(120,129)(121,130)(122,131)(123,132)(124,133)(125,134)(126,135); 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*s1*s2, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*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*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.