Net topology

epu-a

Ingested production record from rcsr+mofplus. Per-field provenance in field_sources.

JSON · mfpx

108 vertices and 180 edges in the unit cell. 46 of them leave the cell and continue into a neighbouring one; those are drawn in the accent colour and end at a hollow node. Squares are vertices of coordination 5 or more, circles of 4 or fewer. Drag to rotate, or focus the figure and use the arrow keys.

Crystallographic description

Spacegroup
R-3m (No. 166)
Cell lengths
a = 6.9459 Å, b = 6.9459 Å, c = 8.8033 Å
Cell angles
α = 90.00°, β = 90.00°, γ = 120.00°
Atoms in cell
108
Transitivity pqrs
4, 8, *, *
Catenated
no
No, computed from the graph of the net itself rather than read off its name: mofpp.periodicity v1 finds a single copy, so it is not interpenetrated on the MOF+ deposit, the graph of the uploaded topology file. Interpenetration is counted here as the number of separate copies of the net that share one repeat unit, so this is a measurement of the topology and not a marker in a string.

Canonical key

Systre key
3 1 2 0 0 0 1 3 0 0 0 1 4 0 0 0 1 5 0 0 0 2 6 0 0 0 2 7 0 0 0 2 8 0 0 0 3 7 0 0 0 3 9 0 0 0 3 10 0 0 0 4 8 0 0 0 4 11 0 0 0 4 12 0 0 0 5 13 0 0 0 5 14 0 0 0 6 15 0 0 0 6 16 0 0 0 7 17 0 0 0 7 18 0 0 0 8 19 0 0 0 8 20 0 0 0 9 15 1 0 0 9 18 0 0 0 9 21 0 0 0 10 22 0 0 0 10 23 0 0 0 11 20 0 0 0 11 21 0 0 0 11 24 0 0 0 12 17 0 1 0 12 25 0 0 0 13 14 0 0 0 13 26 0 0 0 14 20 0 0 1 15 16 0 0 0 16 27 0 0 0 17 25 0 -1 0 18 28 0 0 0 18 29 0 0 0 19 30 0 0 0 19 31 0 0 0 20 29 0 0 0 21 29 0 0 0 21 30 1 0 0 22 23 0 0 0 22 32 0 0 0 23 29 0 0 1 24 28 0 1 0 24 33 0 0 0 25 34 0 0 0 26 34 0 0 0 26 35 0 0 0 27 32 -1 0 0 27 34 0 -1 0 28 33 0 -1 0 30 31 0 0 0 31 35 0 0 -1 32 36 0 0 0 33 36 0 1 -1 35 36 -1 1 0
(rcsr)The canonical Systre key, copied verbatim from the local RCSR Systre archive of 2019-06-01 — and corroborated here rather than carried on the word of the archive alone. Systre 19.6.0 was run on the MOF+ deposit, the graph of the uploaded topology file and computed the same key, character for character, so two independent statements of the canonical form of this net agree. The computed key is served under topology.symmetry with the graph it was computed from and the version that computed it. The checksum beside this key is still the one the archive carries, copied from the same block and neither computed nor verified here.
Checksum
8d3130103069c3cd5e3cd0679028cead (rcsr)

Vertices

The mapping of coordination sequences onto vertex classes that the source supplied was checked against a walk over the periodic topology of the net itself, one walk per vertex class, and agreed. The sequences are the values the source supplied; the walk settled nothing but which class each one describes.

Corroborated: 108 of 108 stored symbols were recomputed from the topology of the net itself and agree, entry for entry. A vertex symbol of this collection names the shortest cycle at each angle of a vertex, and mofpp.rings v2 (mofplus-deposit) walks those cycles on the deposit graph. The strings shown are still the values the source supplied; what was checked is that they are the values this net has.

Site symmetry. 108 of 108 vertex rows carry one, attributed to computed:mofpp.site_symmetry-v1 (spglib-2.7.0, mofplus-deposit). The site symmetry on each vertex row is the point group of the operations of the net's ideal space group that leave that vertex where it is — its Wyckoff position in the net's maximum-symmetry embedding. It is a property of the net, not of any material built on it, and it is what says whether a four-coordinated vertex is tetrahedral (-43m) or square-planar (4/mmm) — a distinction the coordination number cannot make. Computed in R-3m, setting H, by mofpp.site_symmetry v1 with spglib 2.7.0, from the embedding Systre 19.6.0 computed on the mofplus-deposit. spglib determined the same space group from those coordinates independently, which is a check of two different computations against each other rather than a restatement.

One row per distinct vertex. The coordination sequence counts how many vertices lie at each topological distance; the vertex symbol names the shortest ring at each angle of the vertex; the site symmetry is the vertex's Wyckoff position in the net's maximum-symmetry embedding. The three columns do not carry the same warrant: which of them was corroborated, which was not, and which was computed here, is stated above the table.
# Coordination Site symmetry Vertex symbol Coordination sequence
0 3 26.8.83 6 9 13 22 37 57 74 87 110
1 3 26.8.83 6 9 13 22 37 57 74 87 110
2 3 26.8.83 6 9 13 22 37 57 74 87 110
3 3 26.8.83 6 9 13 22 37 57 74 87 110
4 3 26.8.83 6 9 13 22 37 57 74 87 110
5 3 26.8.83 6 9 13 22 37 57 74 87 110
6 3 26.8.83 6 9 13 22 37 57 74 87 110
7 3 26.8.83 6 9 13 22 37 57 74 87 110
8 3 26.8.83 6 9 13 22 37 57 74 87 110
9 3 26.8.83 6 9 13 22 37 57 74 87 110
10 3 26.8.83 6 9 13 22 37 57 74 87 110
11 3 26.8.83 6 9 13 22 37 57 74 87 110
12 3 26.8.83 6 9 13 22 37 57 74 87 110
13 3 26.8.83 6 9 13 22 37 57 74 87 110
14 3 26.8.83 6 9 13 22 37 57 74 87 110
15 3 26.8.83 6 9 13 22 37 57 74 87 110
16 3 26.8.83 6 9 13 22 37 57 74 87 110
17 3 26.8.83 6 9 13 22 37 57 74 87 110
18 3 23.8.83 4 10 19 26 39 50 74 103 126
19 3 23.8.83 4 10 19 26 39 50 74 103 126
20 3 23.8.83 4 10 19 26 39 50 74 103 126
21 3 23.8.83 4 10 19 26 39 50 74 103 126
22 3 23.8.83 4 10 19 26 39 50 74 103 126
23 3 23.8.83 4 10 19 26 39 50 74 103 126
24 3 23.8.83 4 10 19 26 39 50 74 103 126
25 3 23.8.83 4 10 19 26 39 50 74 103 126
26 3 23.8.83 4 10 19 26 39 50 74 103 126
27 3 23.8.83 4 10 19 26 39 50 74 103 126
28 3 23.8.83 4 10 19 26 39 50 74 103 126
29 3 23.8.83 4 10 19 26 39 50 74 103 126
30 3 23.8.83 4 10 19 26 39 50 74 103 126
31 3 23.8.83 4 10 19 26 39 50 74 103 126
32 3 23.8.83 4 10 19 26 39 50 74 103 126
33 3 23.8.83 4 10 19 26 39 50 74 103 126
34 3 23.8.83 4 10 19 26 39 50 74 103 126
35 3 23.8.83 4 10 19 26 39 50 74 103 126
36 3 13.8.83 5 12 22 29 41 53 79 109 130
37 3 13.8.83 5 12 22 29 41 53 79 109 130
38 3 13.8.83 5 12 22 29 41 53 79 109 130
39 3 13.8.83 5 12 22 29 41 53 79 109 130
40 3 13.8.83 5 12 22 29 41 53 79 109 130
41 3 13.8.83 5 12 22 29 41 53 79 109 130
42 3 13.8.83 5 12 22 29 41 53 79 109 130
43 3 13.8.83 5 12 22 29 41 53 79 109 130
44 3 13.8.83 5 12 22 29 41 53 79 109 130
45 3 13.8.83 5 12 22 29 41 53 79 109 130
46 3 13.8.83 5 12 22 29 41 53 79 109 130
47 3 13.8.83 5 12 22 29 41 53 79 109 130
48 3 13.8.83 5 12 22 29 41 53 79 109 130
49 3 13.8.83 5 12 22 29 41 53 79 109 130
50 3 13.8.83 5 12 22 29 41 53 79 109 130
51 3 13.8.83 5 12 22 29 41 53 79 109 130
52 3 13.8.83 5 12 22 29 41 53 79 109 130
53 3 13.8.83 5 12 22 29 41 53 79 109 130
54 3 13.8.83 5 12 22 29 41 53 79 109 130
55 3 13.8.83 5 12 22 29 41 53 79 109 130
56 3 13.8.83 5 12 22 29 41 53 79 109 130
57 3 13.8.83 5 12 22 29 41 53 79 109 130
58 3 13.8.83 5 12 22 29 41 53 79 109 130
59 3 13.8.83 5 12 22 29 41 53 79 109 130
60 3 13.8.83 5 12 22 29 41 53 79 109 130
61 3 13.8.83 5 12 22 29 41 53 79 109 130
62 3 13.8.83 5 12 22 29 41 53 79 109 130
63 3 13.8.83 5 12 22 29 41 53 79 109 130
64 3 13.8.83 5 12 22 29 41 53 79 109 130
65 3 13.8.83 5 12 22 29 41 53 79 109 130
66 3 13.8.83 5 12 22 29 41 53 79 109 130
67 3 13.8.83 5 12 22 29 41 53 79 109 130
68 3 13.8.83 5 12 22 29 41 53 79 109 130
69 3 13.8.83 5 12 22 29 41 53 79 109 130
70 3 13.8.83 5 12 22 29 41 53 79 109 130
71 3 13.8.83 5 12 22 29 41 53 79 109 130
72 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
73 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
74 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
75 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
76 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
77 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
78 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
79 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
80 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
81 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
82 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
83 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
84 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
85 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
86 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
87 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
88 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
89 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
90 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
91 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
92 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
93 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
94 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
95 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
96 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
97 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
98 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
99 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
100 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
101 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
102 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
103 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
104 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
105 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
106 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125
107 4 14.4.6(2).8.8.10(2)4 9 15 21 30 45 66 88 105 125

Computed topology

Computed here from the quotient graph of the net itself, not transcribed from either source: periodicity, symmetry, invariants and rings, on the MOF+ deposit, the graph of the uploaded topology file and the RCSR archive key, the canonical key the archive states, by mofpp.invariants 2, mofpp.periodicity 1, mofpp.rings 2, mofpp.site_symmetry spglib-2.7.0 systre-19.6.0 v1 and systre 19.6.0 sha256:0d272e98a1a21669bc67a809b95c014ba2a2fb39a6fd2147039201216ab0d48d options:--systreKey wrapper:2. Each basis is analysed on its own and the results are never merged, because a MOF+ deposit and an RCSR archive key are two different graphs that usually describe the same net and sometimes do not. The transitivity r and s are computed by nothing in this project: they count the faces and the tiles of a natural tiling, and none is derived here. That is a measured limit rather than a job not yet done. The Gavrog library this project runs Systre from was tried on 2026-09-12: for a 3-periodic net it has no route from a net to a tiling at all, and for a 2-periodic net it has one that works, whose result is a plane tiling with faces and no tiles and so a transitivity triple rather than an r and an s. This block therefore states p and q and leaves r and s unknown rather than filling them. Every entry carries the tool, its version and input_checksum, the checksum of the graph that was actually analysed, so that a result computed from the graph this record holds now can be told from one computed before it changed. Nothing here rebuilds a graph to check that, so no entry below is claimed to be current.

Periodicity — the MOF+ deposit, the graph of the uploaded topology file

Periodicity (mofplus-deposit)
3-periodic
One connected net (mofplus-deposit)
yes
Interpenetration (mofplus-deposit)
1 copy
Computed by (mofplus-deposit)
mofpp.periodicity 1 — ok

Periodicity — the RCSR archive key, the canonical key the archive states

Periodicity (rcsr-archive-key)
3-periodic
One connected net (rcsr-archive-key)
yes
Interpenetration (rcsr-archive-key)
1 copy
Computed by (rcsr-archive-key)
mofpp.periodicity 1 — ok

Symmetry — the MOF+ deposit, the graph of the uploaded topology file

Systre found one connected net in the repeat unit, so the group, the kinds of node and edge, and the key below describe that net.

Ideal space group (mofplus-deposit)
R-3m (No. 166) (hexagonal setting)
Transitivity p, q (mofplus-deposit)
4, 8 Kinds of node and of edge. r and s count the faces and tiles of a natural tiling, and none is derived here: the library this site runs Systre from cannot produce one for a 3-periodic net at all, and a 2-periodic net tiles the plane, which has faces and no tiles. They stay unknown rather than being filled.
Point-group order (mofplus-deposit)
12
Repeat-unit factor (mofplus-deposit)
3
RCSR identification (mofplus-deposit)
epu-a
Computed Systre key (mofplus-deposit)
3 1 2 0 0 0 1 3 0 0 0 1 4 0 0 0 1 5 0 0 0 2 6 0 0 0 2 7 0 0 0 2 8 0 0 0 3 7 0 0 0 3 9 0 0 0 3 10 0 0 0 4 8 0 0 0 4 11 0 0 0 4 12 0 0 0 5 13 0 0 0 5 14 0 0 0 6 15 0 0 0 6 16 0 0 0 7 17 0 0 0 7 18 0 0 0 8 19 0 0 0 8 20 0 0 0 9 15 1 0 0 9 18 0 0 0 9 21 0 0 0 10 22 0 0 0 10 23 0 0 0 11 20 0 0 0 11 21 0 0 0 11 24 0 0 0 12 17 0 1 0 12 25 0 0 0 13 14 0 0 0 13 26 0 0 0 14 20 0 0 1 15 16 0 0 0 16 27 0 0 0 17 25 0 -1 0 18 28 0 0 0 18 29 0 0 0 19 30 0 0 0 19 31 0 0 0 20 29 0 0 0 21 29 0 0 0 21 30 1 0 0 22 23 0 0 0 22 32 0 0 0 23 29 0 0 1 24 28 0 1 0 24 33 0 0 0 25 34 0 0 0 26 34 0 0 0 26 35 0 0 0 27 32 -1 0 0 27 34 0 -1 0 28 33 0 -1 0 30 31 0 0 0 31 35 0 0 -1 32 36 0 0 0 33 36 0 1 -1 35 36 -1 1 0
Key against the archive (mofplus-deposit)
the same key, character for character
TD10 as Systre prints it (mofplus-deposit)
477
Computed by (symmetry, mofplus-deposit)
systre 19.6.0 sha256:0d272e98a1a21669bc67a809b95c014ba2a2fb39a6fd2147039201216ab0d48d options:--systreKey wrapper:2 — ok

Invariants — the MOF+ deposit, the graph of the uploaded topology file

TD10, exact (mofplus-deposit)
476.6666666666667
Genus (mofplus-deposit)
25
Shells walked (mofplus-deposit)
10
Computed by (invariants, mofplus-deposit)
mofpp.invariants 2 — ok

Invariants — the RCSR archive key, the canonical key the archive states

TD10, exact (rcsr-archive-key)
476.6666666666667
Genus (rcsr-archive-key)
25
Shells walked (rcsr-archive-key)
10
Computed by (invariants, rcsr-archive-key)
mofpp.invariants 2 — ok

Rings — the MOF+ deposit, the graph of the uploaded topology file

Net point symbol (mofplus-deposit)
(3.8^2)3(6.8^2)(4^2.6.8^2.10)2
Longest ring searched (mofplus-deposit)
40
Computed by (rings, mofplus-deposit)
mofpp.rings 2 — ok
Computed from the graph itself, one row per set of vertices carrying the same symbols. The cycle symbol follows the MOF+ convention — the shortest cycle at each angle — and is the one comparable with the stored column above; the RCSR ring symbol names the shortest ring at each angle, with * where none exists within the bound, and is a different quantity.
Vertices Cycle symbol (MOF+ convention) RCSR ring symbol Point symbol Coordination sequence
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 176.8.8 6.8.8 6.8^2 3 6 9 13 22 37 57 74 87 110
18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 353.8.8 3.8.8 3.8^2 3 4 10 19 26 39 50 74 103 126
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 713.8.8 3.8.8 3.8^2 3 5 12 22 29 41 53 79 109 130
72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 1074.4.6(2).8.8.10(2) 4.4.6.8.8.16(4) 4^2.6.8^2.10 4 9 15 21 30 45 66 88 105 125

Rings — the RCSR archive key, the canonical key the archive states

Net point symbol (rcsr-archive-key)
(3.8^2)3(6.8^2)(4^2.6.8^2.10)2
Longest ring searched (rcsr-archive-key)
40
Computed by (rings, rcsr-archive-key)
mofpp.rings 2 — ok
Computed from the graph itself, one row per set of vertices carrying the same symbols. The cycle symbol follows the MOF+ convention — the shortest cycle at each angle — and is the one comparable with the stored column above; the RCSR ring symbol names the shortest ring at each angle, with * where none exists within the bound, and is a different quantity.
Vertices Cycle symbol (MOF+ convention) RCSR ring symbol Point symbol Coordination sequence
0, 1, 2, 3, 6, 7, 8, 10, 17, 19, 20, 284.4.6(2).8.8.10(2) 4.4.6.8.8.16(4) 4^2.6.8^2.10 4 9 15 21 30 45 66 88 105 125
4, 5, 9, 11, 13, 14, 16, 18, 22, 23, 27, 293.8.8 3.8.8 3.8^2 3 5 12 22 29 41 53 79 109 130
12, 15, 21, 24, 30, 323.8.8 3.8.8 3.8^2 3 4 10 19 26 39 50 74 103 126
25, 26, 31, 33, 34, 356.8.8 6.8.8 6.8^2 3 6 9 13 22 37 57 74 87 110

Cross-checks

Name against the computed key
corroborated-by-systre-key
Stored symbols against the computed ones
corroborated: 108 of 108 vertex rows agree with mofpp.rings v2 (mofplus-deposit).
Stored sequences against the computed ones
corroborated: 108 of 108 vertex rows agree with mofpp.invariants v2 (mofplus-deposit), compared on the stored length.
Catenation against the name heuristic
No; agrees with the computed value

Provenance

Source
rcsr+mofplus — reconciled from both, field by field
Identifier at the source
epu-a
Retrieved
2026-09-09
Licence
CC BY 4.0 — verified from MOF++ project decision, CONTEXT §6 (Licensing): MOF+ is this group's own service, so nets retrieved from it are the project's own data to license, and the project licenses its data CC BY 4.0. No third-party grant is claimed..
Published
yes

Position in the collection

RCSR index
615 (derived) Derived by this site, not published by RCSR: the 1-based position of the symbol in the ascending ASCII-lexicographic ordering of the 2930 symbols in the RCSR Systre archive of 2019-06-01. RCSR does not number its nets; this is our ordering of their symbols and nothing more.
Complexity rank
2206 The order the ingest processed this net in, simplest first. A different number from the RCSR index above, meaning a different thing.