Net topology

nbd

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

JSON · mfpx

204 vertices and 408 edges in the unit cell. 98 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 = 4.4200 Å, b = 4.4200 Å, c = 21.4170 Å
Cell angles
α = 90.00°, β = 90.00°, γ = 120.00°
Atoms in cell
204
Transitivity pqrs
12, 19, *, *
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 11 0 0 0 4 12 0 0 0 4 13 0 0 0 5 14 0 0 0 5 15 0 0 0 5 16 0 0 0 6 11 0 0 0 6 17 0 0 0 6 18 0 0 0 7 19 0 0 0 7 20 0 0 0 8 14 0 0 0 8 21 0 0 0 8 22 0 0 0 9 23 0 0 0 9 24 0 0 0 9 25 0 0 0 10 26 0 0 0 10 27 0 0 0 10 28 0 0 0 11 29 0 0 0 11 30 0 0 0 12 22 1 0 0 12 24 0 0 0 12 31 0 0 0 13 15 0 0 0 13 32 0 0 0 13 33 0 0 0 14 31 -1 0 0 14 34 0 0 0 15 35 0 0 0 15 36 0 0 0 16 17 0 1 0 16 28 0 0 0 16 29 0 1 0 17 31 -1 -1 0 17 37 0 0 0 18 21 0 0 0 18 33 -1 -1 0 18 38 0 0 0 19 23 0 0 0 19 37 0 0 0 19 39 0 0 0 20 26 0 0 0 20 40 0 0 0 20 41 0 0 0 21 36 -1 -1 0 21 42 0 0 0 22 29 -1 0 0 22 41 0 0 0 23 43 0 0 0 23 44 0 0 0 24 41 1 0 0 24 45 0 0 0 25 27 0 0 0 25 46 0 0 0 25 47 0 0 0 26 45 -1 0 0 26 48 0 0 0 27 49 0 0 0 27 50 0 0 0 28 37 0 1 0 28 43 0 1 0 29 36 0 -1 0 30 32 0 0 0 30 38 0 0 0 30 51 0 0 0 31 33 0 0 0 32 52 0 0 0 32 53 0 0 0 33 54 0 0 0 34 35 0 0 0 34 42 0 0 0 34 54 -1 0 0 35 52 0 0 0 35 55 0 0 0 36 51 0 1 0 37 45 -1 -1 0 38 56 0 0 0 38 57 0 0 0 39 40 0 0 0 39 47 -1 -1 0 39 58 0 0 0 40 50 -1 -1 0 40 59 0 0 0 41 43 -1 0 0 42 57 0 0 0 42 60 0 0 0 43 50 0 -1 0 44 46 0 0 0 44 58 0 0 0 44 61 0 0 0 45 47 0 0 0 46 62 0 0 0 46 63 0 0 0 47 64 0 0 0 48 49 0 0 0 48 59 0 0 0 48 64 -1 0 0 49 62 0 0 0 49 65 0 0 0 50 61 0 1 0 51 55 0 -1 0 51 60 1 0 0 52 57 0 0 0 52 66 0 0 0 53 54 0 0 0 53 60 1 0 0 53 67 0 0 0 54 56 1 1 0 55 56 0 1 0 55 63 0 0 1 56 62 0 -1 1 57 65 0 -1 1 58 67 -1 0 -1 58 68 0 0 0 59 66 -1 0 -1 59 67 -1 0 -1 60 68 0 0 1 61 65 0 -1 0 61 66 0 0 -1 62 67 -1 0 -1 63 64 0 0 0 63 66 0 0 -1 64 68 1 1 0 65 68 0 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
ecf65cc26432058c23954b4fa12ad20b (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: 204 of 204 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. 204 of 204 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 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
1 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
2 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
3 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
4 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
5 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
6 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
7 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
8 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
9 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
10 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
11 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
12 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
13 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
14 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
15 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
16 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
17 4 m5.5.5.5.5.64 12 25 42 70 92 126 173 217 271
18 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
19 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
20 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
21 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
22 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
23 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
24 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
25 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
26 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
27 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
28 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
29 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
30 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
31 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
32 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
33 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
34 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
35 4 m5.5.5.5.5.64 12 25 43 66 93 129 171 217 270
36 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
37 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
38 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
39 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
40 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
41 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
42 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
43 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
44 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
45 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
46 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
47 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
48 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
49 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
50 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
51 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
52 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
53 4 m5.5.5.5.5.64 12 23 41 64 95 130 167 214 271
54 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
55 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
56 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
57 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
58 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
59 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
60 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
61 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
62 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
63 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
64 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
65 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
66 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
67 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
68 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
69 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
70 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
71 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
72 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
73 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
74 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
75 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
76 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
77 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
78 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
79 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
80 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
81 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
82 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
83 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
84 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
85 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
86 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
87 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
88 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
89 4 14.5.5.5.6.64 11 24 41 63 92 129 173 218 266
90 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
91 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
92 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
93 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
94 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
95 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
96 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
97 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
98 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
99 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
100 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
101 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
102 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
103 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
104 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
105 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
106 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
107 4 m5.5.5.5.5.64 12 23 41 65 91 130 172 211 262
108 4 3m5.5.5.5.5.54 12 24 39 66 103 130 162 213 270
109 4 3m5.5.5.5.5.54 12 24 39 66 103 130 162 213 270
110 4 3m5.5.5.5.5.54 12 24 39 66 103 130 162 213 270
111 4 3m5.5.5.5.5.54 12 24 39 66 103 130 162 213 270
112 4 3m5.5.5.5.5.54 12 24 39 66 103 130 162 213 270
113 4 3m5.5.5.5.5.54 12 24 39 66 103 130 162 213 270
114 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
115 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
116 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
117 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
118 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
119 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
120 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
121 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
122 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
123 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
124 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
125 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
126 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
127 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
128 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
129 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
130 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
131 4 m5.5.5.5.5.64 12 25 43 67 96 131 173 218 270
132 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
133 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
134 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
135 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
136 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
137 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
138 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
139 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
140 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
141 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
142 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
143 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
144 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
145 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
146 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
147 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
148 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
149 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
150 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
151 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
152 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
153 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
154 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
155 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
156 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
157 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
158 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
159 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
160 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
161 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
162 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
163 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
164 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
165 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
166 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
167 4 15.5.5.5.5.64 12 25 43 68 94 132 176 219 267
168 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
169 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
170 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
171 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
172 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
173 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
174 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
175 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
176 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
177 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
178 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
179 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
180 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
181 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
182 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
183 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
184 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
185 4 m5.5.5.5.5.54 12 24 39 66 100 128 168 211 265
186 4 3m5.5.5.5.5.54 12 24 36 61 107 136 156 207 259
187 4 3m5.5.5.5.5.54 12 24 36 61 107 136 156 207 259
188 4 3m5.5.5.5.5.54 12 24 36 61 107 136 156 207 259
189 4 3m5.5.5.5.5.54 12 24 36 61 107 136 156 207 259
190 4 3m5.5.5.5.5.54 12 24 36 61 107 136 156 207 259
191 4 3m5.5.5.5.5.54 12 24 36 61 107 136 156 207 259
192 4 3m5.5.5.5.5.54 12 24 36 61 101 133 162 207 261
193 4 3m5.5.5.5.5.54 12 24 36 61 101 133 162 207 261
194 4 3m5.5.5.5.5.54 12 24 36 61 101 133 162 207 261
195 4 3m5.5.5.5.5.54 12 24 36 61 101 133 162 207 261
196 4 3m5.5.5.5.5.54 12 24 36 61 101 133 162 207 261
197 4 3m5.5.5.5.5.54 12 24 36 61 101 133 162 207 261
198 4 3m5.5.5.5.5.54 12 24 36 64 106 129 156 216 268
199 4 3m5.5.5.5.5.54 12 24 36 64 106 129 156 216 268
200 4 3m5.5.5.5.5.54 12 24 36 64 106 129 156 216 268
201 4 3m5.5.5.5.5.54 12 24 36 64 106 129 156 216 268
202 4 3m5.5.5.5.5.54 12 24 36 64 106 129 156 216 268
203 4 3m5.5.5.5.5.54 12 24 36 64 106 129 156 216 268

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)
12, 19 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)
nbd
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 11 0 0 0 4 12 0 0 0 4 13 0 0 0 5 14 0 0 0 5 15 0 0 0 5 16 0 0 0 6 11 0 0 0 6 17 0 0 0 6 18 0 0 0 7 19 0 0 0 7 20 0 0 0 8 14 0 0 0 8 21 0 0 0 8 22 0 0 0 9 23 0 0 0 9 24 0 0 0 9 25 0 0 0 10 26 0 0 0 10 27 0 0 0 10 28 0 0 0 11 29 0 0 0 11 30 0 0 0 12 22 1 0 0 12 24 0 0 0 12 31 0 0 0 13 15 0 0 0 13 32 0 0 0 13 33 0 0 0 14 31 -1 0 0 14 34 0 0 0 15 35 0 0 0 15 36 0 0 0 16 17 0 1 0 16 28 0 0 0 16 29 0 1 0 17 31 -1 -1 0 17 37 0 0 0 18 21 0 0 0 18 33 -1 -1 0 18 38 0 0 0 19 23 0 0 0 19 37 0 0 0 19 39 0 0 0 20 26 0 0 0 20 40 0 0 0 20 41 0 0 0 21 36 -1 -1 0 21 42 0 0 0 22 29 -1 0 0 22 41 0 0 0 23 43 0 0 0 23 44 0 0 0 24 41 1 0 0 24 45 0 0 0 25 27 0 0 0 25 46 0 0 0 25 47 0 0 0 26 45 -1 0 0 26 48 0 0 0 27 49 0 0 0 27 50 0 0 0 28 37 0 1 0 28 43 0 1 0 29 36 0 -1 0 30 32 0 0 0 30 38 0 0 0 30 51 0 0 0 31 33 0 0 0 32 52 0 0 0 32 53 0 0 0 33 54 0 0 0 34 35 0 0 0 34 42 0 0 0 34 54 -1 0 0 35 52 0 0 0 35 55 0 0 0 36 51 0 1 0 37 45 -1 -1 0 38 56 0 0 0 38 57 0 0 0 39 40 0 0 0 39 47 -1 -1 0 39 58 0 0 0 40 50 -1 -1 0 40 59 0 0 0 41 43 -1 0 0 42 57 0 0 0 42 60 0 0 0 43 50 0 -1 0 44 46 0 0 0 44 58 0 0 0 44 61 0 0 0 45 47 0 0 0 46 62 0 0 0 46 63 0 0 0 47 64 0 0 0 48 49 0 0 0 48 59 0 0 0 48 64 -1 0 0 49 62 0 0 0 49 65 0 0 0 50 61 0 1 0 51 55 0 -1 0 51 60 1 0 0 52 57 0 0 0 52 66 0 0 0 53 54 0 0 0 53 60 1 0 0 53 67 0 0 0 54 56 1 1 0 55 56 0 1 0 55 63 0 0 1 56 62 0 -1 1 57 65 0 -1 1 58 67 -1 0 -1 58 68 0 0 0 59 66 -1 0 -1 59 67 -1 0 -1 60 68 0 0 1 61 65 0 -1 0 61 66 0 0 -1 62 67 -1 0 -1 63 64 0 0 0 63 66 0 0 -1 64 68 1 1 0 65 68 0 1 0
Key against the archive (mofplus-deposit)
the same key, character for character
TD10 as Systre prints it (mofplus-deposit)
1026
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)
1026.2058823529412
Genus (mofplus-deposit)
69
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)
1026.2058823529412
Genus (rcsr-archive-key)
69
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)
(4.5^3.6^2)6(5^5.6)21(5^6)7
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, 175.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 25 42 70 92 126 173 217 271
18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 355.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 25 43 66 93 129 171 217 270
36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 535.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 23 41 64 95 130 167 214 271
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, 894.5.5.5.6.6 4.5.5.5.6.6 4.5^3.6^2 4 11 24 41 63 92 129 173 218 266
90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 1075.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 23 41 65 91 130 172 211 262
108, 109, 110, 111, 112, 1135.5.5.5.5.5 5.5.5.5.5.5 5^6 4 12 24 39 66 103 130 162 213 270
114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 1315.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 25 43 67 96 131 173 218 270
132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 1675.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 25 43 68 94 132 176 219 267
168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 1855.5.5.5.5.5 5.5.5.5.5.5 5^6 4 12 24 39 66 100 128 168 211 265
186, 187, 188, 189, 190, 1915.5.5.5.5.5 5.5.5.5.5.5 5^6 4 12 24 36 61 107 136 156 207 259
192, 193, 194, 195, 196, 1975.5.5.5.5.5 5.5.5.5.5.5 5^6 4 12 24 36 61 101 133 162 207 261
198, 199, 200, 201, 202, 2035.5.5.5.5.5 5.5.5.5.5.5 5^6 4 12 24 36 64 106 129 156 216 268

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

Net point symbol (rcsr-archive-key)
(4.5^3.6^2)6(5^5.6)21(5^6)7
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, 6, 11, 15, 16, 21, 23, 27, 36, 404.5.5.5.6.6 4.5.5.5.6.6 4.5^3.6^2 4 11 24 41 63 92 129 173 218 266
3, 5, 9, 19, 28, 445.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 23 41 64 95 130 167 214 271
4, 7, 8, 18, 30, 425.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 23 41 65 91 130 172 211 262
10, 255.5.5.5.5.5 5.5.5.5.5.5 5^6 4 12 24 36 64 106 129 156 216 268
12, 17, 26, 35, 39, 465.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 25 42 70 92 126 173 217 271
13, 225.5.5.5.5.5 5.5.5.5.5.5 5^6 4 12 24 36 61 101 133 162 207 261
14, 20, 24, 32, 38, 495.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 25 43 66 93 129 171 217 270
29, 475.5.5.5.5.5 5.5.5.5.5.5 5^6 4 12 24 39 66 103 130 162 213 270
31, 37, 48, 50, 58, 635.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 25 43 67 96 131 173 218 270
33, 435.5.5.5.5.5 5.5.5.5.5.5 5^6 4 12 24 36 61 107 136 156 207 259
34, 41, 45, 53, 57, 605.5.5.5.5.5 5.5.5.5.5.5 5^6 4 12 24 39 66 100 128 168 211 265
51, 52, 54, 55, 56, 59, 61, 62, 64, 65, 66, 675.5.5.5.5.6 5.5.5.5.5.6 5^5.6 4 12 25 43 68 94 132 176 219 267

Cross-checks

Name against the computed key
corroborated-by-systre-key
Stored symbols against the computed ones
corroborated: 204 of 204 vertex rows agree with mofpp.rings v2 (mofplus-deposit).
Stored sequences against the computed ones
corroborated: 204 of 204 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
nbd
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
1373 (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
2345 The order the ingest processed this net in, simplest first. A different number from the RCSR index above, meaning a different thing.