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Net topology

pyd

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

JSON · mfpx

128 vertices and 192 edges in the unit cell. 45 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
Fd-3m (No. 227)
Cell lengths
a = 7.7274 Å, b = 7.7274 Å, c = 7.7274 Å
Cell angles
α = 90.00°, β = 90.00°, γ = 90.00°
Atoms in cell
128
Transitivity pqrs
2, 2, *, *
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 2 5 0 0 0 2 6 0 0 0 3 7 0 0 0 3 8 0 0 0 4 9 0 0 0 4 10 0 0 0 5 11 0 0 0 5 12 0 0 0 6 13 0 0 0 6 14 0 0 0 7 13 1 0 0 7 15 0 0 0 8 16 0 0 0 8 17 0 0 0 9 17 0 0 0 9 18 0 0 0 10 11 0 1 0 10 19 0 0 0 11 20 0 0 0 12 21 0 0 0 12 22 0 0 0 13 23 0 0 0 14 21 -1 1 0 14 24 0 0 0 15 25 0 0 0 15 26 0 0 0 16 22 0 0 0 16 26 0 0 1 17 27 0 0 0 18 24 0 0 0 18 28 0 0 0 19 25 0 0 0 19 28 0 0 -1 20 29 0 0 0 20 30 0 0 0 21 31 0 0 0 22 29 0 0 0 23 30 0 0 0 23 32 0 0 0 24 32 0 0 0 25 30 0 0 -1 26 31 0 1 0 27 29 0 1 0 27 32 1 0 0 28 31 0 1 1
(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
a05dff8f41479749ba013c0fed7c8b67 (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: 128 of 128 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. 128 of 128 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 Fd-3m, setting 2, 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 m6.8.83 6 11 18 26 37 55 79 107 140
1 3 m6.8.83 6 11 18 26 37 55 79 107 140
2 3 m6.8.83 6 11 18 26 37 55 79 107 140
3 3 m6.8.83 6 11 18 26 37 55 79 107 140
4 3 m6.8.83 6 11 18 26 37 55 79 107 140
5 3 m6.8.83 6 11 18 26 37 55 79 107 140
6 3 m6.8.83 6 11 18 26 37 55 79 107 140
7 3 m6.8.83 6 11 18 26 37 55 79 107 140
8 3 m6.8.83 6 11 18 26 37 55 79 107 140
9 3 m6.8.83 6 11 18 26 37 55 79 107 140
10 3 m6.8.83 6 11 18 26 37 55 79 107 140
11 3 m6.8.83 6 11 18 26 37 55 79 107 140
12 3 m6.8.83 6 11 18 26 37 55 79 107 140
13 3 m6.8.83 6 11 18 26 37 55 79 107 140
14 3 m6.8.83 6 11 18 26 37 55 79 107 140
15 3 m6.8.83 6 11 18 26 37 55 79 107 140
16 3 m6.8.83 6 11 18 26 37 55 79 107 140
17 3 m6.8.83 6 11 18 26 37 55 79 107 140
18 3 m6.8.83 6 11 18 26 37 55 79 107 140
19 3 m6.8.83 6 11 18 26 37 55 79 107 140
20 3 m6.8.83 6 11 18 26 37 55 79 107 140
21 3 m6.8.83 6 11 18 26 37 55 79 107 140
22 3 m6.8.83 6 11 18 26 37 55 79 107 140
23 3 m6.8.83 6 11 18 26 37 55 79 107 140
24 3 m6.8.83 6 11 18 26 37 55 79 107 140
25 3 m6.8.83 6 11 18 26 37 55 79 107 140
26 3 m6.8.83 6 11 18 26 37 55 79 107 140
27 3 m6.8.83 6 11 18 26 37 55 79 107 140
28 3 m6.8.83 6 11 18 26 37 55 79 107 140
29 3 m6.8.83 6 11 18 26 37 55 79 107 140
30 3 m6.8.83 6 11 18 26 37 55 79 107 140
31 3 m6.8.83 6 11 18 26 37 55 79 107 140
32 3 m6.8.83 6 11 18 26 37 55 79 107 140
33 3 m6.8.83 6 11 18 26 37 55 79 107 140
34 3 m6.8.83 6 11 18 26 37 55 79 107 140
35 3 m6.8.83 6 11 18 26 37 55 79 107 140
36 3 m6.8.83 6 11 18 26 37 55 79 107 140
37 3 m6.8.83 6 11 18 26 37 55 79 107 140
38 3 m6.8.83 6 11 18 26 37 55 79 107 140
39 3 m6.8.83 6 11 18 26 37 55 79 107 140
40 3 m6.8.83 6 11 18 26 37 55 79 107 140
41 3 m6.8.83 6 11 18 26 37 55 79 107 140
42 3 m6.8.83 6 11 18 26 37 55 79 107 140
43 3 m6.8.83 6 11 18 26 37 55 79 107 140
44 3 m6.8.83 6 11 18 26 37 55 79 107 140
45 3 m6.8.83 6 11 18 26 37 55 79 107 140
46 3 m6.8.83 6 11 18 26 37 55 79 107 140
47 3 m6.8.83 6 11 18 26 37 55 79 107 140
48 3 m6.8.83 6 11 18 26 37 55 79 107 140
49 3 m6.8.83 6 11 18 26 37 55 79 107 140
50 3 m6.8.83 6 11 18 26 37 55 79 107 140
51 3 m6.8.83 6 11 18 26 37 55 79 107 140
52 3 m6.8.83 6 11 18 26 37 55 79 107 140
53 3 m6.8.83 6 11 18 26 37 55 79 107 140
54 3 m6.8.83 6 11 18 26 37 55 79 107 140
55 3 m6.8.83 6 11 18 26 37 55 79 107 140
56 3 m6.8.83 6 11 18 26 37 55 79 107 140
57 3 m6.8.83 6 11 18 26 37 55 79 107 140
58 3 m6.8.83 6 11 18 26 37 55 79 107 140
59 3 m6.8.83 6 11 18 26 37 55 79 107 140
60 3 m6.8.83 6 11 18 26 37 55 79 107 140
61 3 m6.8.83 6 11 18 26 37 55 79 107 140
62 3 m6.8.83 6 11 18 26 37 55 79 107 140
63 3 m6.8.83 6 11 18 26 37 55 79 107 140
64 3 m6.8.83 6 11 18 26 37 55 79 107 140
65 3 m6.8.83 6 11 18 26 37 55 79 107 140
66 3 m6.8.83 6 11 18 26 37 55 79 107 140
67 3 m6.8.83 6 11 18 26 37 55 79 107 140
68 3 m6.8.83 6 11 18 26 37 55 79 107 140
69 3 m6.8.83 6 11 18 26 37 55 79 107 140
70 3 m6.8.83 6 11 18 26 37 55 79 107 140
71 3 m6.8.83 6 11 18 26 37 55 79 107 140
72 3 m6.8.83 6 11 18 26 37 55 79 107 140
73 3 m6.8.83 6 11 18 26 37 55 79 107 140
74 3 m6.8.83 6 11 18 26 37 55 79 107 140
75 3 m6.8.83 6 11 18 26 37 55 79 107 140
76 3 m6.8.83 6 11 18 26 37 55 79 107 140
77 3 m6.8.83 6 11 18 26 37 55 79 107 140
78 3 m6.8.83 6 11 18 26 37 55 79 107 140
79 3 m6.8.83 6 11 18 26 37 55 79 107 140
80 3 m6.8.83 6 11 18 26 37 55 79 107 140
81 3 m6.8.83 6 11 18 26 37 55 79 107 140
82 3 m6.8.83 6 11 18 26 37 55 79 107 140
83 3 m6.8.83 6 11 18 26 37 55 79 107 140
84 3 m6.8.83 6 11 18 26 37 55 79 107 140
85 3 m6.8.83 6 11 18 26 37 55 79 107 140
86 3 m6.8.83 6 11 18 26 37 55 79 107 140
87 3 m6.8.83 6 11 18 26 37 55 79 107 140
88 3 m6.8.83 6 11 18 26 37 55 79 107 140
89 3 m6.8.83 6 11 18 26 37 55 79 107 140
90 3 m6.8.83 6 11 18 26 37 55 79 107 140
91 3 m6.8.83 6 11 18 26 37 55 79 107 140
92 3 m6.8.83 6 11 18 26 37 55 79 107 140
93 3 m6.8.83 6 11 18 26 37 55 79 107 140
94 3 m6.8.83 6 11 18 26 37 55 79 107 140
95 3 m6.8.83 6 11 18 26 37 55 79 107 140
96 3 3m8.8.83 6 12 18 27 39 54 81 105 135
97 3 3m8.8.83 6 12 18 27 39 54 81 105 135
98 3 3m8.8.83 6 12 18 27 39 54 81 105 135
99 3 3m8.8.83 6 12 18 27 39 54 81 105 135
100 3 3m8.8.83 6 12 18 27 39 54 81 105 135
101 3 3m8.8.83 6 12 18 27 39 54 81 105 135
102 3 3m8.8.83 6 12 18 27 39 54 81 105 135
103 3 3m8.8.83 6 12 18 27 39 54 81 105 135
104 3 3m8.8.83 6 12 18 27 39 54 81 105 135
105 3 3m8.8.83 6 12 18 27 39 54 81 105 135
106 3 3m8.8.83 6 12 18 27 39 54 81 105 135
107 3 3m8.8.83 6 12 18 27 39 54 81 105 135
108 3 3m8.8.83 6 12 18 27 39 54 81 105 135
109 3 3m8.8.83 6 12 18 27 39 54 81 105 135
110 3 3m8.8.83 6 12 18 27 39 54 81 105 135
111 3 3m8.8.83 6 12 18 27 39 54 81 105 135
112 3 3m8.8.83 6 12 18 27 39 54 81 105 135
113 3 3m8.8.83 6 12 18 27 39 54 81 105 135
114 3 3m8.8.83 6 12 18 27 39 54 81 105 135
115 3 3m8.8.83 6 12 18 27 39 54 81 105 135
116 3 3m8.8.83 6 12 18 27 39 54 81 105 135
117 3 3m8.8.83 6 12 18 27 39 54 81 105 135
118 3 3m8.8.83 6 12 18 27 39 54 81 105 135
119 3 3m8.8.83 6 12 18 27 39 54 81 105 135
120 3 3m8.8.83 6 12 18 27 39 54 81 105 135
121 3 3m8.8.83 6 12 18 27 39 54 81 105 135
122 3 3m8.8.83 6 12 18 27 39 54 81 105 135
123 3 3m8.8.83 6 12 18 27 39 54 81 105 135
124 3 3m8.8.83 6 12 18 27 39 54 81 105 135
125 3 3m8.8.83 6 12 18 27 39 54 81 105 135
126 3 3m8.8.83 6 12 18 27 39 54 81 105 135
127 3 3m8.8.83 6 12 18 27 39 54 81 105 135

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)
Fd-3m (No. 227) (second origin choice)
Transitivity p, q (mofplus-deposit)
2, 2 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)
pyd
Computed Systre key (mofplus-deposit)
3 1 2 0 0 0 1 3 0 0 0 1 4 0 0 0 2 5 0 0 0 2 6 0 0 0 3 7 0 0 0 3 8 0 0 0 4 9 0 0 0 4 10 0 0 0 5 11 0 0 0 5 12 0 0 0 6 13 0 0 0 6 14 0 0 0 7 13 1 0 0 7 15 0 0 0 8 16 0 0 0 8 17 0 0 0 9 17 0 0 0 9 18 0 0 0 10 11 0 1 0 10 19 0 0 0 11 20 0 0 0 12 21 0 0 0 12 22 0 0 0 13 23 0 0 0 14 21 -1 1 0 14 24 0 0 0 15 25 0 0 0 15 26 0 0 0 16 22 0 0 0 16 26 0 0 1 17 27 0 0 0 18 24 0 0 0 18 28 0 0 0 19 25 0 0 0 19 28 0 0 -1 20 29 0 0 0 20 30 0 0 0 21 31 0 0 0 22 29 0 0 0 23 30 0 0 0 23 32 0 0 0 24 32 0 0 0 25 30 0 0 -1 26 31 0 1 0 27 29 0 1 0 27 32 1 0 0 28 31 0 1 1
Key against the archive (mofplus-deposit)
the same key, character for character
TD10 as Systre prints it (mofplus-deposit)
483
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)
482.5
Genus (mofplus-deposit)
17
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)
482.5
Genus (rcsr-archive-key)
17
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)
(6.8^2)3(8^3)
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, 956.8.8 6.8.8 6.8^2 3 6 11 18 26 37 55 79 107 140
96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 1278.8.8 8.8.8 8^3 3 6 12 18 27 39 54 81 105 135

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

Net point symbol (rcsr-archive-key)
(6.8^2)3(8^3)
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, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14, 16, 18, 19, 21, 22, 23, 24, 25, 27, 28, 30, 316.8.8 6.8.8 6.8^2 3 6 11 18 26 37 55 79 107 140
1, 6, 9, 15, 17, 20, 26, 298.8.8 8.8.8 8^3 3 6 12 18 27 39 54 81 105 135

Cross-checks

Name against the computed key
corroborated-by-systre-key
Stored symbols against the computed ones
corroborated: 128 of 128 vertex rows agree with mofpp.rings v2 (mofplus-deposit).
Stored sequences against the computed ones
corroborated: 128 of 128 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
pyd
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
1598 (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
2244 The order the ingest processed this net in, simplest first. A different number from the RCSR index above, meaning a different thing.