Overview
- Group
- SmallGroup(1280,1116447)
- Rank
- 3
- Schläfli Type
- {20,4}
- Vertices, edges, …
- 160, 320, 32
- Order of s0s1s2
- 20
- 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
64-fold
80-fold
160-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)^2*s1*(s2*s1*s0)^2*s2*s1> of order 2
16 facets
- 16 of {20}*40
80 vertex figures
- 80 of {4}*8
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2> of order 2
16 facets
- 16 of {20}*40
80 vertex figures
- 80 of {4}*8
P/N, where N=<(s0*s1)^3*(s2*s1*s0)^3*s2> of order 2
16 facets
- 16 of {20}*40
80 vertex figures
- 80 of {4}*8
P/N, where N=<(s0*s1)^6*s0*s2*(s1*s0)^3*s2*s1> of order 2
16 facets
- 16 of {20}*40
80 vertex figures
- 80 of {4}*8
P/N, where N=<(s0*s1)^7*(s0*s2*s1)^3> of order 2
16 facets
- 16 of {20}*40
80 vertex figures
- 80 of {4}*8
P/N, where N=<(s0*s1)^7*(s0*s2*s1)^2*s0*s1*s2> of order 2
16 facets
- 16 of {20}*40
80 vertex figures
- 80 of {4}*8
P/N, where N=<(s0*s1)^6*(s0*s2*s1)^3*s0*s1*s2> of order 2
16 facets
- 16 of {20}*40
80 vertex figures
- 80 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*(s1*s0)^3*s2*s1> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s1*s2)^2, (s0*s1)^3*(s2*s1*s0)^3*s2> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<s0*s2*(s1*s0)^2*s1*s2*s1*s0*s2*s1> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1> of order 4
8 facets
- 8 of {20}*40
56 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*(s2*s1*s0)^2*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*(s1*s0)^2*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*s1*s2*s1*s0*s2*s1> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<(s1*s0*s2)^2*s1*s0*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, (s0*s1)^7*(s0*s2*s1)^2*s0*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1)^3*(s2*s1*s0)^3*s2, (s0*s1)^7*(s0*s2*s1)^3> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1)^3*(s2*s1*s0)^3*s1*s2*s1, (s0*s1)^7*(s0*s2*s1)^2*s0*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1)^3*(s2*s1*s0)^3*s2, (s0*s1)^6*s0*s2*(s1*s0)^3*s2*s1> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, (s0*s1)^7*s0*s2*(s1*s0)^2*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2, (s0*s1)^6*s0*s2*(s1*s0)^3*s2*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s1*s2, (s0*s1)^6*s0*s2*(s1*s0)^2*s2*s1*s0*s2*s1> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2, (s0*s1)^6*s0*s2*(s1*s0)^3*s2*s1> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, (s0*s1)^6*s0*s2*(s1*s0)^3*s2*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*(s1*s2)^2, (s0*s1)^7*(s0*s2*s1)^2*s0*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, (s0*s1)^6*s0*s2*(s1*s0)^3*s2*s1> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*s2, (s0*s1)^6*s0*s2*(s1*s0)^3*s2*s1> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s1*s0)^4*s2*(s1*s0)^3*s2*s1> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^7*(s0*s2*s1)^3*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^7*s0*s2*(s1*s0)^2*s2*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^7*s0*s2*(s1*s0)^2*s1*s2> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s1*s2)^2, (s0*s1)^6*(s0*s2*s1)^3*s0*s1*s2> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<s0*s1*s2*s1*s0*s2, (s0*s1)^7*(s0*s2*s1)^2*s0*s1*s2> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^6*s0*s2*(s1*s0)^3*s2*s1> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^7*s0*s2*(s1*s0)^2*s2*s1*s2> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s1, (s0*s1)^6*s0*s2*(s1*s0)^3*s2*s1> of order 4
8 facets
- 8 of {20}*40
48 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^7*(s0*s2*s1)^3> of order 4
8 facets
- 8 of {20}*40
40 vertex figures
- 40 of {4}*8
P/N, where N=<(s1*s2)^2, s0*s1*s2*s1*s0*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1> of order 8
4 facets
- 4 of {20}*40
32 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*s1*s2*s1*s0*s2*s1*s2, (s0*s1)^2*(s2*s1*s0)^2*s2> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2, (s0*s1)^2*(s2*s1*s0)^2*s2> of order 8
4 facets
- 4 of {20}*40
20 vertex figures
- 20 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*s2*(s1*s0)^2*(s1*s2)^2> of order 8
4 facets
- 4 of {20}*40
28 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1, (s0*s1)^3*s0*s2*(s1*s0)^2*s2> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1, (s0*s1)^3*(s0*s2*s1)^2*s0*s2> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*s1*s0*s2*s1*s2> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*s2*s1*s0*s1*s2> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^7*s0*s2*(s1*s0)^2*s1*s2> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2, (s0*s1)^7*s0*s2*(s1*s0)^2*s2*s1*s2> of order 8
4 facets
- 4 of {20}*40
20 vertex figures
- 20 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s0*s1)^2*(s2*s1*s0)^2*s2, (s0*s1)^8*s0*s2*s1*s0*s1*s2> of order 8
4 facets
- 4 of {20}*40
20 vertex figures
- 20 of {4}*8
P/N, where N=<s0*s1*s2*s1*s0*s2, s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^7*s0*s2*(s1*s0)^2*s2*s1*s2> of order 8
4 facets
- 4 of {20}*40
28 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1, (s0*s1)^6*s0*s2*(s1*s0)^3*s2*s1> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, (s0*s1)^8*s0*s2*s1*s0*s1*s2> of order 8
4 facets
- 4 of {20}*40
20 vertex figures
- 20 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1, (s0*s1)^8*s0*s2*s1*s0*s1*s2> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0)^2*s1*(s2*s1*s0)^2*s1, (s0*s1)^8*(s0*s2*s1)^2*s2> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<s0*s1*s2*(s1*s0)^2*s1*s2*s1*s0*s1*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, (s0*s1)^7*s0*s2*(s1*s0)^2*s1*s2> of order 8
4 facets
- 4 of {20}*40
20 vertex figures
- 20 of {4}*8
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*(s2*s1*s0)^2*(s1*s2)^2, (s0*s1)^7*s0*s2*(s1*s0)^2*s1*s2> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<(s0*s1)^2*(s2*s1*s0)^2*s2, (s1*s0)^2*s1*(s2*s1*s0)^2*s2*s1, (s0*s1)^8*s0*s2*s1*s0*s1*s2> of order 8
4 facets
- 4 of {20}*40
20 vertex figures
- 20 of {4}*8
P/N, where N=<(s0*s1*s2*s1)^2, s1*s0*s1*s2*s1*s0*s2*s1, (s0*s1)^2*s2*(s1*s0)^2*s2> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<(s1*s0)^2*s1*(s2*s1*s0)^2*s1, (s0*s1)^3*s0*s2*(s1*s0)^2*s2, s1*s0*s2*(s1*s0)^2*s2*s1*s0*s2*s1*s2> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, (s0*s2*s1)^2*s0*(s1*s2)^2, (s1*s0)^4*s2*(s1*s0)^3*s2*s1> of order 8
4 facets
- 4 of {20}*40
24 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 51, 52)( 55, 56)( 59, 60)( 63, 64)( 65,121)( 66,122)( 67,124)( 68,123)( 69,125)( 70,126)( 71,128)( 72,127)( 73,113)( 74,114)( 75,116)( 76,115)( 77,117)( 78,118)( 79,120)( 80,119)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,105)( 90,106)( 91,108)( 92,107)( 93,109)( 94,110)( 95,112)( 96,111);; s1 := ( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,100)( 10, 99)( 11, 98)( 12, 97)( 13,104)( 14,103)( 15,102)( 16,101)( 17, 60)( 18, 59)( 19, 58)( 20, 57)( 21, 64)( 22, 63)( 23, 62)( 24, 61)( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 96)( 30, 95)( 31, 94)( 32, 93)( 33, 76)( 34, 75)( 35, 74)( 36, 73)( 37, 80)( 38, 79)( 39, 78)( 40, 77)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49,116)( 50,115)( 51,114)( 52,113)( 53,120)( 54,119)( 55,118)( 56,117)( 65, 68)( 66, 67)( 69, 72)( 70, 71)( 81,124)( 82,123)( 83,122)( 84,121)( 85,128)( 86,127)( 87,126)( 88,125)(105,108)(106,107)(109,112)(110,111);; s2 := ( 1, 61)( 2, 62)( 3, 63)( 4, 64)( 5, 57)( 6, 58)( 7, 59)( 8, 60)( 9, 53)( 10, 54)( 11, 55)( 12, 56)( 13, 49)( 14, 50)( 15, 51)( 16, 52)( 17, 45)( 18, 46)( 19, 47)( 20, 48)( 21, 41)( 22, 42)( 23, 43)( 24, 44)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 65,125)( 66,126)( 67,127)( 68,128)( 69,121)( 70,122)( 71,123)( 72,124)( 73,117)( 74,118)( 75,119)( 76,120)( 77,113)( 78,114)( 79,115)( 80,116)( 81,109)( 82,110)( 83,111)( 84,112)( 85,105)( 86,106)( 87,107)( 88,108)( 89,101)( 90,102)( 91,103)( 92,104)( 93, 97)( 94, 98)( 95, 99)( 96,100);; 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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(128)!( 3, 4)( 7, 8)( 11, 12)( 15, 16)( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 33, 41)( 34, 42)( 35, 44)( 36, 43)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 51, 52)( 55, 56)( 59, 60)( 63, 64)( 65,121)( 66,122)( 67,124)( 68,123)( 69,125)( 70,126)( 71,128)( 72,127)( 73,113)( 74,114)( 75,116)( 76,115)( 77,117)( 78,118)( 79,120)( 80,119)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,105)( 90,106)( 91,108)( 92,107)( 93,109)( 94,110)( 95,112)( 96,111); s1 := Sym(128)!( 1, 4)( 2, 3)( 5, 8)( 6, 7)( 9,100)( 10, 99)( 11, 98)( 12, 97)( 13,104)( 14,103)( 15,102)( 16,101)( 17, 60)( 18, 59)( 19, 58)( 20, 57)( 21, 64)( 22, 63)( 23, 62)( 24, 61)( 25, 92)( 26, 91)( 27, 90)( 28, 89)( 29, 96)( 30, 95)( 31, 94)( 32, 93)( 33, 76)( 34, 75)( 35, 74)( 36, 73)( 37, 80)( 38, 79)( 39, 78)( 40, 77)( 41, 44)( 42, 43)( 45, 48)( 46, 47)( 49,116)( 50,115)( 51,114)( 52,113)( 53,120)( 54,119)( 55,118)( 56,117)( 65, 68)( 66, 67)( 69, 72)( 70, 71)( 81,124)( 82,123)( 83,122)( 84,121)( 85,128)( 86,127)( 87,126)( 88,125)(105,108)(106,107)(109,112)(110,111); s2 := Sym(128)!( 1, 61)( 2, 62)( 3, 63)( 4, 64)( 5, 57)( 6, 58)( 7, 59)( 8, 60)( 9, 53)( 10, 54)( 11, 55)( 12, 56)( 13, 49)( 14, 50)( 15, 51)( 16, 52)( 17, 45)( 18, 46)( 19, 47)( 20, 48)( 21, 41)( 22, 42)( 23, 43)( 24, 44)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 65,125)( 66,126)( 67,127)( 68,128)( 69,121)( 70,122)( 71,123)( 72,124)( 73,117)( 74,118)( 75,119)( 76,120)( 77,113)( 78,114)( 79,115)( 80,116)( 81,109)( 82,110)( 83,111)( 84,112)( 85,105)( 86,106)( 87,107)( 88,108)( 89,101)( 90,102)( 91,103)( 92,104)( 93, 97)( 94, 98)( 95, 99)( 96,100); 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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*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 >;
References
None.
to this polytope.