diff --git a/Data/Interpolation/Poromechanics/Identity_2.hhdata b/Data/Interpolation/Poromechanics/Identity_2x2.hhdata
similarity index 100%
rename from Data/Interpolation/Poromechanics/Identity_2.hhdata
rename to Data/Interpolation/Poromechanics/Identity_2x2.hhdata
diff --git a/Data/Interpolation/Poromechanics/Identity_3.hhdata b/Data/Interpolation/Poromechanics/Identity_3x3.hhdata
similarity index 100%
rename from Data/Interpolation/Poromechanics/Identity_3.hhdata
rename to Data/Interpolation/Poromechanics/Identity_3x3.hhdata
diff --git a/Data/Interpolation/Poromechanics/Identity_5.hhdata b/Data/Interpolation/Poromechanics/Identity_5x5.hhdata
similarity index 100%
rename from Data/Interpolation/Poromechanics/Identity_5.hhdata
rename to Data/Interpolation/Poromechanics/Identity_5x5.hhdata
diff --git a/Data/Interpolation/Poromechanics/Identity_6.hhdata b/Data/Interpolation/Poromechanics/Identity_6x6.hhdata
similarity index 100%
rename from Data/Interpolation/Poromechanics/Identity_6.hhdata
rename to Data/Interpolation/Poromechanics/Identity_6x6.hhdata
diff --git a/Data/Interpolation/Poromechanics/Identity_6x6x6.hhdata b/Data/Interpolation/Poromechanics/Identity_6x6x6.hhdata
new file mode 100644
index 0000000000000000000000000000000000000000..61a8522d68140dfc2656eaf1804e8dfc565ab285
--- /dev/null
+++ b/Data/Interpolation/Poromechanics/Identity_6x6x6.hhdata
@@ -0,0 +1,344 @@
+# Vertex index in mesh 1 / vertex index in mesh 2
+1 1
+2 2
+3 3
+4 4
+5 5
+6 6
+7 7
+8 8
+9 9
+10 10
+11 11
+12 12
+13 13
+14 14
+15 15
+16 16
+17 17
+18 18
+19 19
+20 20
+21 21
+22 22
+23 23
+24 24
+25 25
+26 26
+27 27
+28 28
+29 29
+30 30
+31 31
+32 32
+33 33
+34 34
+35 35
+36 36
+37 37
+38 38
+39 39
+40 40
+41 41
+42 42
+43 43
+44 44
+45 45
+46 46
+47 47
+48 48
+49 49
+50 50
+51 51
+52 52
+53 53
+54 54
+55 55
+56 56
+57 57
+58 58
+59 59
+60 60
+61 61
+62 62
+63 63
+64 64
+65 65
+66 66
+67 67
+68 68
+69 69
+70 70
+71 71
+72 72
+73 73
+74 74
+75 75
+76 76
+77 77
+78 78
+79 79
+80 80
+81 81
+82 82
+83 83
+84 84
+85 85
+86 86
+87 87
+88 88
+89 89
+90 90
+91 91
+92 92
+93 93
+94 94
+95 95
+96 96
+97 97
+98 98
+99 99
+100 100
+101 101
+102 102
+103 103
+104 104
+105 105
+106 106
+107 107
+108 108
+109 109
+110 110
+111 111
+112 112
+113 113
+114 114
+115 115
+116 116
+117 117
+118 118
+119 119
+120 120
+121 121
+122 122
+123 123
+124 124
+125 125
+126 126
+127 127
+128 128
+129 129
+130 130
+131 131
+132 132
+133 133
+134 134
+135 135
+136 136
+137 137
+138 138
+139 139
+140 140
+141 141
+142 142
+143 143
+144 144
+145 145
+146 146
+147 147
+148 148
+149 149
+150 150
+151 151
+152 152
+153 153
+154 154
+155 155
+156 156
+157 157
+158 158
+159 159
+160 160
+161 161
+162 162
+163 163
+164 164
+165 165
+166 166
+167 167
+168 168
+169 169
+170 170
+171 171
+172 172
+173 173
+174 174
+175 175
+176 176
+177 177
+178 178
+179 179
+180 180
+181 181
+182 182
+183 183
+184 184
+185 185
+186 186
+187 187
+188 188
+189 189
+190 190
+191 191
+192 192
+193 193
+194 194
+195 195
+196 196
+197 197
+198 198
+199 199
+200 200
+201 201
+202 202
+203 203
+204 204
+205 205
+206 206
+207 207
+208 208
+209 209
+210 210
+211 211
+212 212
+213 213
+214 214
+215 215
+216 216
+217 217
+218 218
+219 219
+220 220
+221 221
+222 222
+223 223
+224 224
+225 225
+226 226
+227 227
+228 228
+229 229
+230 230
+231 231
+232 232
+233 233
+234 234
+235 235
+236 236
+237 237
+238 238
+239 239
+240 240
+241 241
+242 242
+243 243
+244 244
+245 245
+246 246
+247 247
+248 248
+249 249
+250 250
+251 251
+252 252
+253 253
+254 254
+255 255
+256 256
+257 257
+258 258
+259 259
+260 260
+261 261
+262 262
+263 263
+264 264
+265 265
+266 266
+267 267
+268 268
+269 269
+270 270
+271 271
+272 272
+273 273
+274 274
+275 275
+276 276
+277 277
+278 278
+279 279
+280 280
+281 281
+282 282
+283 283
+284 284
+285 285
+286 286
+287 287
+288 288
+289 289
+290 290
+291 291
+292 292
+293 293
+294 294
+295 295
+296 296
+297 297
+298 298
+299 299
+300 300
+301 301
+302 302
+303 303
+304 304
+305 305
+306 306
+307 307
+308 308
+309 309
+310 310
+311 311
+312 312
+313 313
+314 314
+315 315
+316 316
+317 317
+318 318
+319 319
+320 320
+321 321
+322 322
+323 323
+324 324
+325 325
+326 326
+327 327
+328 328
+329 329
+330 330
+331 331
+332 332
+333 333
+334 334
+335 335
+336 336
+337 337
+338 338
+339 339
+340 340
+341 341
+342 342
+343 343
\ No newline at end of file
diff --git a/Data/Interpolation/Poromechanics/Identity_8.hhdata b/Data/Interpolation/Poromechanics/Identity_8x8.hhdata
similarity index 100%
rename from Data/Interpolation/Poromechanics/Identity_8.hhdata
rename to Data/Interpolation/Poromechanics/Identity_8x8.hhdata
diff --git a/Data/Lua/demo_input_poromechanics.lua b/Data/Lua/demo_input_poromechanics.lua
index f352ac61fc215f479f7e9150cbc9c86e65d1311f..0444f3e4e00ce32e5f9d20854482a494dd84494d 100644
--- a/Data/Lua/demo_input_poromechanics.lua
+++ b/Data/Lua/demo_input_poromechanics.lua
@@ -1776,7 +1776,7 @@ PenalizationPorosity = {
 -- File that gives for each vertex on the first mesh on the interface the index of the equivalent vertex in
 -- the second mesh.
 -- Expected format: "VALUE"
-interpolation_file = "${HOME}/Codes/HappyHeart/Data/Interpolation/Poromechanics/Identity_6.hhdata"
+interpolation_file = "${HOME}/Codes/HappyHeart/Data/Interpolation/Poromechanics/Identity_6x6.hhdata"
 
 -- Internal friction.
 -- Expected format: VALUE
diff --git a/Data/Lua/demo_input_poromechanics_3d.lua b/Data/Lua/demo_input_poromechanics_3d.lua
index 08370ac3533536335cdf6b94911bb93be8f28f53..3c202b43d602318fa8fb4f24402fefc99341ef00 100644
--- a/Data/Lua/demo_input_poromechanics_3d.lua
+++ b/Data/Lua/demo_input_poromechanics_3d.lua
@@ -558,7 +558,7 @@ Domain21 = {
     -- dimensions.
     -- Expected format: {VALUE1, VALUE2, ...}
     -- Constraint: ops_in(v, {0, 1, 2, 3})
-    dimension_list = { 2 },
+    dimension_list = { 3 },
     
     
     -- List of mesh labels encompassed by the domain. Might be left empty if no restriction at all upon mesh
@@ -1776,7 +1776,7 @@ PenalizationPorosity = {
 -- File that gives for each vertex on the first mesh on the interface the index of the equivalent vertex in
 -- the second mesh.
 -- Expected format: "VALUE"
-interpolation_file = "${HOME}/Codes/HappyHeart/Data/Interpolation/Poromechanics/Identity_6.hhdata"
+interpolation_file = "${HOME}/Codes/HappyHeart/Data/Interpolation/Poromechanics/Identity_6x6x6.hhdata"
 
 -- Internal friction.
 -- Expected format: VALUE
diff --git a/Sources/Geometry/Interpolator/VertexMatching.cpp b/Sources/Geometry/Interpolator/VertexMatching.cpp
index e21a00f0e4d8e38c54bff8def041f5907cb37a24..9f880c37dd921bafc370beaab8811a2e3a33f586 100644
--- a/Sources/Geometry/Interpolator/VertexMatching.cpp
+++ b/Sources/Geometry/Interpolator/VertexMatching.cpp
@@ -99,7 +99,9 @@ namespace HappyHeart
                                           target_end,
                                           target_index);
                 
-                assert(it != target_end);
+                assert(it != target_end && "Check your interpolation file (given in input parameter) is up-to-date... "
+                       "It might also be that  your domains aren't well balanced (typically not the same "
+                       "dimension...");
                 
                 const auto pos = static_cast<std::size_t>(it - target_begin);
                 
diff --git a/Sources/Geometry/Interpolator/VertexMatching.hpp b/Sources/Geometry/Interpolator/VertexMatching.hpp
index 4ad8111a7d5e6b3ee1818ff2e7dbb684064655ca..7fdee88f6b0751cae1dde6174b2b647291e0e26d 100644
--- a/Sources/Geometry/Interpolator/VertexMatching.hpp
+++ b/Sources/Geometry/Interpolator/VertexMatching.hpp
@@ -19,6 +19,8 @@
 
 # include "Core/InputParameter/Geometry/InterpolationFile.hpp"
 
+# include "Geometry/Mesh/GeometricMeshRegion.hpp"
+
 
 namespace HappyHeart
 {
diff --git a/Sources/Operators/NonConformInterpolator/FromVertexMatching.hxx b/Sources/Operators/NonConformInterpolator/FromVertexMatching.hxx
index 88715480126452a383a9cdc8afc33ec59b3bfbfd..77002e995ae3664dc64c0037121dd5f5be6ad059 100644
--- a/Sources/Operators/NonConformInterpolator/FromVertexMatching.hxx
+++ b/Sources/Operators/NonConformInterpolator/FromVertexMatching.hxx
@@ -25,7 +25,7 @@ namespace HappyHeart
                                                const unsigned int source_index,
                                                const unsigned int target_index)
         {
-            MeshNS::InterpolationNS::VertexMatching vertex_matching(input_parameter_data);
+            MeshNS::InterpolationNS::VertexMatching vertex_matching( input_parameter_data);
             
             Construct(vertex_matching,
                       source_index,