Overview
- Group
- SmallGroup(256,5078)
- Rank
- 3
- Schläfli Type
- {8,4}
- Vertices, edges, …
- 32, 64, 16
- Order of s0s1s2
- 8
- Order of s0s1s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Self-Petrie
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
16-fold
32-fold
Covers minimal covers in bold
2-fold
- {16,4}*512a
- {8,8}*512c
- {8,4}*512a
- {8,8}*512f
- {16,4}*512b
- {8,4}*512b
- {8,4}*512c
- {8,8}*512l
- {8,8}*512n
- {16,4}*512c
- {16,4}*512d
3-fold
5-fold
7-fold
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*s0*s2*s1*s0*s1*s2> of order 2
8 facets
- 8 of {8}*16
16 vertex figures
- 16 of {4}*8
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*s1*s2*s1> of order 2
8 facets
- 8 of {8}*16
16 vertex figures
- 16 of {4}*8
P/N, where N=<s1*s0*s1*(s2*s1*s0)^2*(s1*s2)^2> of order 2
8 facets
- 8 of {8}*16
16 vertex figures
- 16 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 {8}*16
10 vertex figures
P/N, where N=<(s0*s1)^2*s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 4
4 facets
- 4 of {8}*16
8 vertex figures
- 8 of {4}*8
P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s0*s2*(s1*s0)^2*s2*s1*s2> of order 4
4 facets
- 4 of {8}*16
8 vertex figures
- 8 of {4}*8
P/N, where N=<(s1*s2)^2, s0*(s1*s0*s2)^2*s1*s0*s1*s2> of order 4
4 facets
- 4 of {8}*16
10 vertex figures
P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1, (s0*s1)^2*s0*s2*s1*s0*s1*s2> of order 4
4 facets
- 4 of {8}*16
8 vertex figures
- 8 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 {8}*16
8 vertex figures
- 8 of {4}*8
Representations
Permutation Representation (GAP)
s0 := ( 1, 65)( 2, 66)( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 71)( 8, 72)( 9, 76)( 10, 75)( 11, 74)( 12, 73)( 13, 80)( 14, 79)( 15, 78)( 16, 77)( 17, 85)( 18, 86)( 19, 87)( 20, 88)( 21, 81)( 22, 82)( 23, 83)( 24, 84)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,101)( 38,102)( 39,103)( 40,104)( 41,108)( 42,107)( 43,106)( 44,105)( 45,112)( 46,111)( 47,110)( 48,109)( 49,117)( 50,118)( 51,119)( 52,120)( 53,113)( 54,114)( 55,115)( 56,116)( 57,128)( 58,127)( 59,126)( 60,125)( 61,124)( 62,123)( 63,122)( 64,121);; s1 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 58)( 54, 57)( 55, 59)( 56, 60)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 97,123)( 98,124)( 99,122)(100,121)(101,127)(102,128)(103,126)(104,125)(105,115)(106,116)(107,114)(108,113)(109,119)(110,120)(111,118)(112,117);; s2 := ( 1, 33)( 2, 34)( 3, 35)( 4, 36)( 5, 37)( 6, 38)( 7, 39)( 8, 40)( 9, 41)( 10, 42)( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 47)( 16, 48)( 17, 51)( 18, 52)( 19, 49)( 20, 50)( 21, 55)( 22, 56)( 23, 53)( 24, 54)( 25, 59)( 26, 60)( 27, 57)( 28, 58)( 29, 63)( 30, 64)( 31, 61)( 32, 62)( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,101)( 70,102)( 71,103)( 72,104)( 73,105)( 74,106)( 75,107)( 76,108)( 77,109)( 78,110)( 79,111)( 80,112)( 81,115)( 82,116)( 83,113)( 84,114)( 85,119)( 86,120)( 87,117)( 88,118)( 89,123)( 90,124)( 91,121)( 92,122)( 93,127)( 94,128)( 95,125)( 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*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(128)!( 1, 65)( 2, 66)( 3, 67)( 4, 68)( 5, 69)( 6, 70)( 7, 71)( 8, 72)( 9, 76)( 10, 75)( 11, 74)( 12, 73)( 13, 80)( 14, 79)( 15, 78)( 16, 77)( 17, 85)( 18, 86)( 19, 87)( 20, 88)( 21, 81)( 22, 82)( 23, 83)( 24, 84)( 25, 96)( 26, 95)( 27, 94)( 28, 93)( 29, 92)( 30, 91)( 31, 90)( 32, 89)( 33, 97)( 34, 98)( 35, 99)( 36,100)( 37,101)( 38,102)( 39,103)( 40,104)( 41,108)( 42,107)( 43,106)( 44,105)( 45,112)( 46,111)( 47,110)( 48,109)( 49,117)( 50,118)( 51,119)( 52,120)( 53,113)( 54,114)( 55,115)( 56,116)( 57,128)( 58,127)( 59,126)( 60,125)( 61,124)( 62,123)( 63,122)( 64,121); s1 := Sym(128)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 17, 21)( 18, 22)( 19, 24)( 20, 23)( 25, 29)( 26, 30)( 27, 32)( 28, 31)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 58)( 54, 57)( 55, 59)( 56, 60)( 65, 81)( 66, 82)( 67, 84)( 68, 83)( 69, 85)( 70, 86)( 71, 88)( 72, 87)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 97,123)( 98,124)( 99,122)(100,121)(101,127)(102,128)(103,126)(104,125)(105,115)(106,116)(107,114)(108,113)(109,119)(110,120)(111,118)(112,117); s2 := Sym(128)!( 1, 33)( 2, 34)( 3, 35)( 4, 36)( 5, 37)( 6, 38)( 7, 39)( 8, 40)( 9, 41)( 10, 42)( 11, 43)( 12, 44)( 13, 45)( 14, 46)( 15, 47)( 16, 48)( 17, 51)( 18, 52)( 19, 49)( 20, 50)( 21, 55)( 22, 56)( 23, 53)( 24, 54)( 25, 59)( 26, 60)( 27, 57)( 28, 58)( 29, 63)( 30, 64)( 31, 61)( 32, 62)( 65, 97)( 66, 98)( 67, 99)( 68,100)( 69,101)( 70,102)( 71,103)( 72,104)( 73,105)( 74,106)( 75,107)( 76,108)( 77,109)( 78,110)( 79,111)( 80,112)( 81,115)( 82,116)( 83,113)( 84,114)( 85,119)( 86,120)( 87,117)( 88,118)( 89,123)( 90,124)( 91,121)( 92,122)( 93,127)( 94,128)( 95,125)( 96,126); poly := sub<Sym(128)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 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 >;
References
None.
to this polytope.