Dentings

Every net with an embedded denting, richest first, showing all of its dentings — one model per symmetry orbit, starting from the undented realization (∅). ×k marks an orbit of k dent sets; gap is the least distance between vertex-disjoint faces, in edge lengths. 47 nets, 195 dentings, every model embedded and certified — regenerated from the dent-walk scan (data/walks/), which walked which vertex subsets can be dented together without breaking the embedding; adding dents in different orders never gave unequal results.

CCCACCACCACCACACAADEBE v=13

∅

{1} ×3 gap 0.548

{2} ×3 gap 0.455

{3} ×3 gap 0.540

{4} gap 0.619

{6} ×3 gap 0.524

{3,5} ×3 gap 0.316

{3,5,10} gap 0.359

CCCACCACCACCACAACADEBE v=13

∅

{1} ×4 gap 0.283

{2} ×2 gap 0.410

{3} ×2 gap 0.515

{4} ×2 gap 0.381

{5} ×2 gap 0.363

{11} gap 0.251

{2,8} gap 0.033

{5,10} gap 0.238

{2,4,8} ×2 gap 0.049

{2,4,8,12} gap 0.055

CCCACCACCACACACAACAAAE v=13

∅

{1} gap 0.657

{2} ×2 gap 0.639

{3} ×2 gap 0.467

{6} ×4 gap 0.414

{8} ×2 gap 0.419

{12} ×2 gap 0.489

{3,5} gap 0.358

{3,12} ×4 gap 0.258

{3,5,12} ×2 gap 0.279

CCCACCACCACACAACAACAAE v=13

∅

{1} ×2 gap 0.369

{2} ×2 gap 0.333

{3} ×2 gap 0.315

{4} ×2 gap 0.301

{5} ×2 gap 0.396

{7} gap 0.455

{1,9} ×2 gap 0.116

CCCACCACACCACACCAABABE v=13

∅

{1} ×2 gap 0.356

{4} ×2 gap 0.239

{6} ×2 gap 0.407

{7} ×2 gap 0.363

{13} gap 0.389

{1,10} gap 0.152

{6,8} gap 0.204

{1,6,8} ×2 gap 0.120

{1,6,8,10} gap 0.069

CCCACCACACCACACCAABAAE v=13

∅

{1} gap 0.436

{4} ×2 gap 0.436

{6} ×2 gap 0.427

{7} gap 0.409

{10} gap 0.337

{12} gap 0.311

{13} gap 0.426

{1,10} gap 0.076

{6,10} ×2 gap 0.088

{7,12} gap 0.109

{6,8,10} gap 0.125

{1,6,8,10} gap 0.063

CCCACCACACCACACACAABBE v=13

∅

{1} gap 0.280

{3} gap 0.249

{4} gap 0.401

{5} gap 0.490

{6} gap 0.332

{7} gap 0.536

{8} gap 0.432

{9} gap 0.422

{11} gap 0.467

{12} gap 0.429

{13} gap 0.451

{5,7} gap 0.269

{5,9} gap 0.265

{7,9} gap 0.225

{5,7,9} gap 0.283

CCCACCACACCACACACAAABE v=13

∅

{4} ×3 gap 0.279

{7} gap 0.707

{1,10} ×3 gap 0.062

CCCACCACACCACACACAAAAE v=13

∅

{2} ×2 gap 0.244

{4} ×2 gap 0.371

{5} ×2 gap 0.510

{9} gap 0.476

{5,9} ×2 gap 0.012

CCCACCACACCACACAACADEE v=13

∅

{1} gap 0.388

{2} gap 0.285

{4} gap 0.340

{7} gap 0.389

{8} gap 0.466

{9} gap 0.263

{11} gap 0.346

{12} gap 0.388

{13} gap 0.422

{2,11} gap 0.174

CCCACCACACCACACAACAAAE v=13

∅

{1} ×2 gap 0.356

{2} ×2 gap 0.305

{4} gap 0.573

{5} ×2 gap 0.511

{6} ×2 gap 0.385

{7} ×2 gap 0.346

{2,11} ×2 gap 0.065

CCCACCACACCACAACACAAAE v=13

∅

{1} ×2 gap 0.279

{2} ×2 gap 0.321

{4} gap 0.381

{5} ×2 gap 0.383

{7} ×2 gap 0.319

{2,11} ×2 gap 0.122

CCCACCACACACACCAACADEE v=13

∅

{1} gap 0.418

{5} gap 0.366

{6} gap 0.481

{8} gap 0.440

{9} gap 0.266

{5,11} gap 0.182

CCCACCACACACACACACAABE v=13

∅

{1} gap 0.263

{5} gap 0.466

{7} ×2 gap 0.291

{10} gap 0.273

{11} ×2 gap 0.370

{12} gap 0.070

{1,10} gap 0.160

CCCACCACACACACACACAAAE v=13

∅

{1} gap 0.303

{5} gap 0.570

{6} ×2 gap 0.355

{7} ×2 gap 0.460

{10} gap 0.314

{1,10} gap 0.060

CCCACCACACACACACAACAAE v=13

∅

{5} ×2 gap 0.348

{7} gap 0.633

{1,9} ×2 gap 0.177

CCCACCACACAACCACACAAAE v=13

CCCACACCACCACACACAAAAE v=13

∅

{4} ×2 gap 0.382

{9} ×2 gap 0.453

{13} gap 0.554

{4,6} gap 0.145

{4,13} ×2 gap 0.073

{4,6,13} gap 0.157

CCCACACCACCACACAACADEE v=13

∅

{8} ×2 gap 0.300

{9} ×2 gap 0.149

{13} gap 0.435

CCCACACCACCACACAACAABE v=13

∅

{6} ×2 gap 0.345

CCCACACCACCACACAACAAAE v=13

∅

{4} gap 0.386

{6} gap 0.311

{8} gap 0.513

{11} gap 0.291

{12} gap 0.397

{13} gap 0.330

CCCACACCACCACACAAACAAE v=13

∅

{4} gap 0.422

{12} gap 0.509

{13} gap 0.349

CCCACACCACACACACCAAABE v=13

∅

{4} ×2 gap 0.324

{6} gap 0.157

CCCACACCACACACACACAABE v=13

∅

{8} gap 0.326

{12} gap 0.169

CCCACACCACACACACAACAAE v=13

∅

{6} gap 0.378

{9} gap 0.532

CCCACACACCACACACACAAAE v=13

∅

{7} gap 0.526

{9} ×2 gap 0.301

{12} gap 0.391

CCCACACACCACACACAACAAE v=13

∅

{7} gap 0.303

{9} gap 0.349

CCCCACCACACACAACAAAE v=12

∅

{1} ×12 gap 0.638

CCCACCACCACACACAAAAE v=12

∅

{1} ×3 gap 0.347

{2} ×6 gap 0.329

{3} ×3 gap 0.493

{3,5} ×3 gap 0.285

{3,5,12} gap 0.328

CCCACCACCACACAACADEE v=12

∅

{1} ×4 gap 0.374

CCCACCACACCACACAAABE v=12

∅

{1} ×2 gap 0.409

{4} ×2 gap 0.573

{6} ×2 gap 0.391

{7} ×2 gap 0.387

{1,10} gap 0.113

CCCACCACACCACACAAAAE v=12

∅

{2} ×2 gap 0.251

{4} ×2 gap 0.329

{6} ×2 gap 0.289

{7} gap 0.264

{9} ×2 gap 0.338

{10} gap 0.177

{12} gap 0.372

CCCACCACACCACAACAABE v=12

∅

{4} ×2 gap 0.377

CCCACCACACACACACAABE v=12

∅

{1} gap 0.247

{7} gap 0.494

{9} gap 0.236

CCCACCACACACACAACAAE v=12

∅

{5} ×2 gap 0.445

CCCACACCACCACACAAABE v=12

∅

{7} ×2 gap 0.390

{9} ×2 gap 0.282

CCCACACCACCACACAAAAE v=12

∅

{9} gap 0.363

{12} gap 0.368

CCCACACCACACACACAAAE v=12

∅

{4} gap 0.281

{6} gap 0.380

{11} gap 0.422

{12} gap 0.284