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Net topology

hal

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

JSON · mfpx

96 vertices and 192 edges in the unit cell. 24 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
Fm-3m (No. 225)
Cell lengths
a = 6.2430 Å, b = 6.2430 Å, c = 6.2430 Å
Cell angles
α = 90.00°, β = 90.00°, γ = 90.00°
Atoms in cell
96
Transitivity pqrs
1, 3, *, *
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 3 0 0 0 2 6 0 0 0 2 7 0 0 0 3 8 0 0 0 3 9 0 0 0 4 10 0 0 0 4 11 0 0 0 4 12 0 0 0 5 12 0 0 0 5 13 0 0 0 5 14 0 0 0 6 15 0 0 0 6 16 0 0 0 6 17 0 0 0 7 15 0 0 0 7 18 0 0 0 7 19 0 0 0 8 20 0 0 0 8 21 0 0 0 8 22 0 0 0 9 22 0 0 0 9 23 0 0 0 9 24 0 0 0 10 11 0 0 0 10 17 1 0 0 10 18 0 0 0 11 21 0 0 0 11 23 1 0 0 12 15 0 0 1 12 22 0 1 0 13 14 0 0 0 13 21 -1 1 0 13 23 0 1 0 14 17 0 0 1 14 18 -1 0 1 15 22 0 1 -1 16 17 0 0 0 16 20 -1 1 0 16 24 0 1 -1 18 19 0 0 0 19 20 0 0 0 19 24 1 0 -1 20 21 0 0 0 23 24 0 0 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
4d917e1972ecff4401573ca89e96857e (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: 96 of 96 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. 96 of 96 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 Fm-3m, setting the conventional one, 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 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
1 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
2 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
3 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
4 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
5 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
6 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
7 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
8 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
9 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
10 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
11 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
12 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
13 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
14 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
15 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
16 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
17 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
18 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
19 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
20 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
21 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
22 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
23 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
24 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
25 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
26 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
27 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
28 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
29 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
30 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
31 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
32 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
33 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
34 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
35 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
36 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
37 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
38 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
39 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
40 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
41 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
42 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
43 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
44 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
45 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
46 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
47 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
48 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
49 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
50 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
51 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
52 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
53 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
54 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
55 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
56 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
57 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
58 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
59 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
60 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
61 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
62 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
63 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
64 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
65 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
66 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
67 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
68 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
69 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
70 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
71 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
72 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
73 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
74 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
75 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
76 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
77 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
78 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
79 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
80 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
81 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
82 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
83 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
84 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
85 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
86 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
87 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
88 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
89 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
90 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
91 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
92 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
93 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
94 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191
95 4 m3.4.6.6.8(2).8(2)4 9 18 30 47 69 91 125 160 191

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)
Fm-3m (No. 225)
Transitivity p, q (mofplus-deposit)
1, 3 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)
48
Repeat-unit factor (mofplus-deposit)
4
RCSR identification (mofplus-deposit)
hal
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 3 0 0 0 2 6 0 0 0 2 7 0 0 0 3 8 0 0 0 3 9 0 0 0 4 10 0 0 0 4 11 0 0 0 4 12 0 0 0 5 12 0 0 0 5 13 0 0 0 5 14 0 0 0 6 15 0 0 0 6 16 0 0 0 6 17 0 0 0 7 15 0 0 0 7 18 0 0 0 7 19 0 0 0 8 20 0 0 0 8 21 0 0 0 8 22 0 0 0 9 22 0 0 0 9 23 0 0 0 9 24 0 0 0 10 11 0 0 0 10 17 1 0 0 10 18 0 0 0 11 21 0 0 0 11 23 1 0 0 12 15 0 0 1 12 22 0 1 0 13 14 0 0 0 13 21 -1 1 0 13 23 0 1 0 14 17 0 0 1 14 18 -1 0 1 15 22 0 1 -1 16 17 0 0 0 16 20 -1 1 0 16 24 0 1 -1 18 19 0 0 0 19 20 0 0 0 19 24 1 0 -1 20 21 0 0 0 23 24 0 0 0
Key against the archive (mofplus-deposit)
the same key, character for character
TD10 as Systre prints it (mofplus-deposit)
745
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)
745.0
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)
745.0
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)
(3.4.6^2.8^2)
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, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 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, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 953.4.6.6.8(2).8(2) 3.4.6.6.8.8 3.4.6^2.8^2 4 9 18 30 47 69 91 125 160 191

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

Net point symbol (rcsr-archive-key)
(3.4.6^2.8^2)
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, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 233.4.6.6.8(2).8(2) 3.4.6.6.8.8 3.4.6^2.8^2 4 9 18 30 47 69 91 125 160 191

Cross-checks

Name against the computed key
corroborated-by-systre-key
Stored symbols against the computed ones
corroborated: 96 of 96 vertex rows agree with mofpp.rings v2 (mofplus-deposit).
Stored sequences against the computed ones
corroborated: 96 of 96 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
hal
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
919 (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
2146 The order the ingest processed this net in, simplest first. A different number from the RCSR index above, meaning a different thing.