Net topology

csi

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

JSON · mfpx

120 vertices and 240 edges in the unit cell. 36 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
Im-3 (No. 204)
Cell lengths
a = 6.2192 Å, b = 6.2192 Å, c = 6.2192 Å
Cell angles
α = 90.00°, β = 90.00°, γ = 90.00°
Atoms in cell
120
Transitivity pqrs
3, 7, *, *
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 5 15 0 0 0 6 16 0 0 0 6 17 0 0 0 6 18 0 0 0 7 19 0 0 0 7 20 0 0 0 8 21 0 0 0 8 22 0 0 0 9 20 0 0 0 9 23 0 0 0 9 24 0 0 0 10 14 0 0 0 10 25 0 0 0 10 26 0 0 0 11 22 0 0 0 11 23 0 0 0 11 27 0 0 0 12 28 0 0 0 12 29 0 0 0 12 30 0 0 0 13 18 0 0 0 13 31 0 0 0 13 32 0 0 0 14 33 0 0 0 14 34 0 0 0 15 30 0 0 0 15 32 0 0 0 15 35 0 0 0 16 36 0 0 0 16 37 0 0 0 16 38 0 0 0 17 21 0 0 0 17 39 0 0 0 17 40 0 0 0 18 38 0 0 0 18 40 0 0 0 19 37 0 0 0 19 41 0 0 0 19 42 0 0 0 20 43 0 0 0 20 44 0 0 0 21 45 0 0 0 21 46 0 0 0 22 44 0 0 0 22 47 0 0 0 23 44 0 0 0 23 48 0 0 0 24 45 1 0 0 24 46 1 0 0 24 49 0 0 0 25 33 0 0 0 25 42 0 0 0 25 50 0 0 0 26 46 1 0 0 26 50 0 0 0 26 51 0 0 0 27 29 0 0 0 27 37 0 1 0 27 42 0 1 0 28 46 0 0 0 28 52 0 0 0 28 53 0 0 0 29 52 0 0 0 29 54 0 0 0 30 53 0 0 0 30 55 0 0 0 31 43 0 0 1 31 52 0 -1 0 31 54 0 -1 0 32 44 0 0 1 32 56 0 0 0 33 54 0 -1 0 33 57 0 0 0 34 36 1 1 1 34 57 0 0 0 34 58 0 0 0 35 36 1 1 1 35 39 1 1 1 35 48 0 0 1 36 49 -1 -1 0 37 58 -1 -1 -1 38 49 -1 -1 0 38 52 0 -1 0 39 55 -1 -1 -1 39 59 0 0 0 40 50 -1 0 0 40 59 0 0 0 41 43 0 0 0 41 53 0 -1 -1 41 55 0 -1 -1 42 59 1 0 0 43 60 0 0 0 45 57 -1 0 -1 45 60 -1 0 0 47 56 0 0 -1 47 57 -1 0 -1 47 58 -1 0 -1 48 49 0 0 0 48 59 1 1 0 50 56 1 0 0 51 53 1 0 0 51 56 1 0 0 51 58 0 0 0 54 60 0 1 1 55 60 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
c7e73c22326a6f9df244c9db46a332eb (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: 120 of 120 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. 120 of 120 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 Im-3, 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 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
1 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
2 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
3 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
4 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
5 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
6 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
7 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
8 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
9 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
10 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
11 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
12 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
13 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
14 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
15 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
16 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
17 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
18 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
19 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
20 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
21 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
22 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
23 4 m4.5.6.6.6.64 11 22 36 52 78 118 150 181 214
24 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
25 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
26 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
27 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
28 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
29 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
30 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
31 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
32 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
33 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
34 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
35 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
36 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
37 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
38 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
39 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
40 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
41 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
42 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
43 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
44 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
45 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
46 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
47 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
48 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
49 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
50 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
51 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
52 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
53 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
54 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
55 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
56 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
57 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
58 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
59 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
60 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
61 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
62 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
63 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
64 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
65 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
66 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
67 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
68 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
69 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
70 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
71 4 14.4.5.6.6.6(2)4 10 20 34 54 78 105 141 180 229
72 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
73 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
74 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
75 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
76 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
77 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
78 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
79 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
80 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
81 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
82 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
83 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
84 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
85 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
86 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
87 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
88 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
89 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
90 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
91 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
92 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
93 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
94 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
95 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
96 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
97 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
98 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
99 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
100 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
101 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
102 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
103 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
104 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
105 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
106 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
107 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
108 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
109 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
110 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
111 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
112 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
113 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
114 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
115 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
116 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
117 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
118 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226
119 4 14.4.5.6.6.6(2)4 10 19 34 54 77 105 136 182 226

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)
Im-3 (No. 204)
Transitivity p, q (mofplus-deposit)
3, 7 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)
24
Repeat-unit factor (mofplus-deposit)
2
RCSR identification (mofplus-deposit)
csi
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 5 15 0 0 0 6 16 0 0 0 6 17 0 0 0 6 18 0 0 0 7 19 0 0 0 7 20 0 0 0 8 21 0 0 0 8 22 0 0 0 9 20 0 0 0 9 23 0 0 0 9 24 0 0 0 10 14 0 0 0 10 25 0 0 0 10 26 0 0 0 11 22 0 0 0 11 23 0 0 0 11 27 0 0 0 12 28 0 0 0 12 29 0 0 0 12 30 0 0 0 13 18 0 0 0 13 31 0 0 0 13 32 0 0 0 14 33 0 0 0 14 34 0 0 0 15 30 0 0 0 15 32 0 0 0 15 35 0 0 0 16 36 0 0 0 16 37 0 0 0 16 38 0 0 0 17 21 0 0 0 17 39 0 0 0 17 40 0 0 0 18 38 0 0 0 18 40 0 0 0 19 37 0 0 0 19 41 0 0 0 19 42 0 0 0 20 43 0 0 0 20 44 0 0 0 21 45 0 0 0 21 46 0 0 0 22 44 0 0 0 22 47 0 0 0 23 44 0 0 0 23 48 0 0 0 24 45 1 0 0 24 46 1 0 0 24 49 0 0 0 25 33 0 0 0 25 42 0 0 0 25 50 0 0 0 26 46 1 0 0 26 50 0 0 0 26 51 0 0 0 27 29 0 0 0 27 37 0 1 0 27 42 0 1 0 28 46 0 0 0 28 52 0 0 0 28 53 0 0 0 29 52 0 0 0 29 54 0 0 0 30 53 0 0 0 30 55 0 0 0 31 43 0 0 1 31 52 0 -1 0 31 54 0 -1 0 32 44 0 0 1 32 56 0 0 0 33 54 0 -1 0 33 57 0 0 0 34 36 1 1 1 34 57 0 0 0 34 58 0 0 0 35 36 1 1 1 35 39 1 1 1 35 48 0 0 1 36 49 -1 -1 0 37 58 -1 -1 -1 38 49 -1 -1 0 38 52 0 -1 0 39 55 -1 -1 -1 39 59 0 0 0 40 50 -1 0 0 40 59 0 0 0 41 43 0 0 0 41 53 0 -1 -1 41 55 0 -1 -1 42 59 1 0 0 43 60 0 0 0 45 57 -1 0 -1 45 60 -1 0 0 47 56 0 0 -1 47 57 -1 0 -1 47 58 -1 0 -1 48 49 0 0 0 48 59 1 1 0 50 56 1 0 0 51 53 1 0 0 51 56 1 0 0 51 58 0 0 0 54 60 0 1 1 55 60 0 1 1
Key against the archive (mofplus-deposit)
the same key, character for character
TD10 as Systre prints it (mofplus-deposit)
855
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)
855.0
Genus (mofplus-deposit)
61
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)
855.0
Genus (rcsr-archive-key)
61
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)
(4.5.6^4)(4^2.5.6^3)4
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, 234.5.6.6.6.6 4.5.6.6.6.6 4.5.6^4 4 11 22 36 52 78 118 150 181 214
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, 714.4.5.6.6.6(2) 4.4.5.6.6.6 4^2.5.6^3 4 10 20 34 54 78 105 141 180 229
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, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 1194.4.5.6.6.6(2) 4.4.5.6.6.6 4^2.5.6^3 4 10 19 34 54 77 105 136 182 226

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

Net point symbol (rcsr-archive-key)
(4.5.6^4)(4^2.5.6^3)4
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, 6, 7, 8, 10, 13, 15, 16, 17, 24, 25, 27, 28, 29, 30, 34, 40, 43, 48, 55, 56, 57, 58, 594.4.5.6.6.6(2) 4.4.5.6.6.6 4^2.5.6^3 4 10 20 34 54 78 105 141 180 229
1, 2, 3, 5, 9, 11, 19, 21, 22, 32, 33, 35, 37, 38, 39, 42, 46, 47, 49, 50, 51, 52, 53, 544.4.5.6.6.6(2) 4.4.5.6.6.6 4^2.5.6^3 4 10 19 34 54 77 105 136 182 226
4, 12, 14, 18, 20, 23, 26, 31, 36, 41, 44, 454.5.6.6.6.6 4.5.6.6.6.6 4.5.6^4 4 11 22 36 52 78 118 150 181 214

Cross-checks

Name against the computed key
corroborated-by-systre-key
Stored symbols against the computed ones
corroborated: 120 of 120 vertex rows agree with mofpp.rings v2 (mofplus-deposit).
Stored sequences against the computed ones
corroborated: 120 of 120 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
csi
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
414 (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
2238 The order the ingest processed this net in, simplest first. A different number from the RCSR index above, meaning a different thing.