Add reference STL models for canonical tensegrity structures + Edison literature surveys (initial + design-gaps follow-up)

[Copilot]

• Verify which DOI links in /home/runner/work/tensegrity-optimization/tensegrity-optimization/models/README.md fail to resolve
• Replace incorrect DOI links with validated DOI/direct publisher links
• Keep the requested figures/tables list unchanged while fixing only citation links
• Commit and push the README corrections

[sgbaird-alt]

@me-madsen maybe we could try printing the other two T4 and icosahedron similar to #35

@copilot noting also that we might want to make the "strings" thicker, since they're not actually strings, but would eventually be TPU.

[Copilot]

@me-madsen maybe we could try printing the other two T4 and icosahedron similar to #35

![](https://github.com/vertical-cloud-lab/tensegrity-optimization/blob/3ffd5e6d158223a4818c60abc0b91ee7c6d8bb...

Bumped the cable diameter from 1.0 mm Ø to 2.4 mm Ø (the same value used for TPU cables in cad/t3-prism/ from #35) and regenerated all three STLs + the preview in 7cc4533. Updated --cable-radius default and the README accordingly.

The T4 + icosahedron print prep (Bambu H2D .gcode.3mf / project .3mf à la #35) is left for @me-madsen as you requested.

[sgbaird-yolo]

@copilot what other tensegrity designs (canonical or not) exist, including especially those in the literature? Use an Edison scientific high effort literature search. Download all artifacts from the Edison query ; wait and fetch the results for this one in same session.

Similar to before, include at least one image of each new type that you found, in case we need to use it later.

[Copilot]

@copilot what other tensegrity designs (canonical or not) exist, including especially those in the literature? Use an Edison scientific high effort literature search. Download all arti...

Submitted Edison LITERATURE_HIGH task fad054b3-fef3-4249-a7d3-151d170efe19 and waited for it in-session (~30 min). Full survey (~60 KB, ~280 lines, 50 cited sources) committed alongside the structured references and full task JSON in df60ac4:

• edison-trajectories/2026-05-09-tensegrity-designs-fad054b3.md
• ...-references.md
• ...-fad054b3.json (full trajectory)

Coverage: Snelson n-prisms (T3/T4/T6/stacked masts), polyhedral & spherical (Jessen's icosahedron, expanded octahedron, truncated tetrahedron, Rimoli/Pajunen truncated-octahedron, Liu et al. cuboctahedron tessellation), Skelton class-k (T-bar / D-bar / class-2 columns), Geiger/Levy cable-domes (Seoul Olympic Hall, Georgia Dome), bio-tensegrity (Levin/Ingber), tensegrity robots (NASA SUPERball v1/v2, Berkeley ULTRA-Spine, TT-3), deployable masts and patents (US 6,441,801; US 6,542,132; US 8,616,328), bistable double-prism (Intrigila 2022), Sabouni-Zawadzka simplex lattices, and topology-generation methods (Tibert/Pellegrino, GA + DNN form-finding 2022/2024).

For the BYU PETG+TPU/H2D project, the survey recommends (top 8): truncated-octahedron cell #1, T3 #2, 4-strut simplex #3, expanded octahedron #4, bistable double-prism #5, cuboctahedron tessellation #6, stacked prismatic column #7, T-bar lattice #8.

Per "include at least one image of each new type", I extended models/generate_stl.py with three new buildable design families (the easiest-to-fabricate of the survey's recommendations) and regenerated the preview as a 6-panel render in df60ac4:

• T6 prism (n=6, twist 60°) — models/stl/6bar_prism.stl
• Stacked T3 column (3-bay Snelson Needle Tower analog with alternating chirality) — models/stl/stacked_t3_column.stl
• Truncated-octahedron tensegrity (Rimoli/Pajunen, 24 nodes / 12 struts / 36 cables — the survey's Get started on this repo #1 energy-absorption pick) — models/stl/truncated_octahedron.stl

The remaining survey designs (cable-domes, biotensegrity, robots, deployable masts, patents, bistable / cuboctahedron metamaterials) are documented in the Edison md with citations to original-paper figures rather than re-rendered, since they require either non-class-1 geometry or external CAD that would need source-paper attribution.

[sgbaird-alt]

@copilot pursue these

cable-domes, biotensegrity, robots, deployable masts, patents, bistable / cuboctahedron metamaterials

You can download whatever software tools you need, CAD or otherwise. If the specifications are unclear, let me know which journal articles you would need to see are or who I could contact about it

[Copilot]

@copilot pursue these

cable-domes, biotensegrity, robots, deployable masts, patents, bistable / cuboctahedron metamaterials
...

Built parametric STLs from first principles for all 7 remaining design families and added an extended preview render in fd32935. Each is exposed as a top-level function in models/generate_stl.py (Python stdlib only, no external CAD dependencies needed):

Design	File	Nodes / Struts / Cables	Function
Geiger cable-dome (Seoul Olympic Hall)	models/stl/geiger_cable_dome.stl	73 / 36 / 132	geiger_cable_dome()
Biotensegrity spine (4 stacked icosahedra; Levin/Flemons/ULTRA-Spine)	models/stl/biotensegrity_spine.stl	48 / 24 / 108	biotensegrity_spine()
NASA SUPERball + payload (robotics)	models/stl/superball_with_payload.stl	24 / 12 / 60	superball_with_payload()
Tibert/Pellegrino deployable mast (6-bay)	models/stl/tibert_pellegrino_mast.stl	21 / 18 / 39	tibert_pellegrino_mast()
US 6,441,801 B1 antenna (Knight et al.)	models/stl/patent_us6441801_antenna.stl	12 / 6 / 18	patent_us6441801_antenna()
Bistable double-prism (Intrigila 2022)	models/stl/bistable_double_prism.stl	9 / 6 / 15	bistable_double_prism()
Cuboctahedron tessellation (Liu et al. 2019, simplified)	models/stl/cuboctahedron_tessellation.stl	13 / 6 / 36	cuboctahedron_tessellation()

These are topology-correct first-principles reconstructions from the geometric specifications cited in the Edison survey — not direct ports of validated FEM meshes from each paper. For production-grade form-found geometry (with prestress states + equilibrium-shape coordinates), I'd want one of the following per design (added a "Caveats and clarifications needed" section to models/README.md):

• Geiger cable-dome — Geiger US Pat. 4,736,553 (1988) full prestress table, or Fu (2005). Possible contact: Feng Fu (City, Univ. of London).
• Biotensegrity spine / ULTRA-Spine — Sabelhaus et al. IEEE RA-L 5(3):3982–3989 (2020) for inter-vertebral cable connectivity, or directly the Berkeley ULTRA-Spine repo. Contact: Andrew Sabelhaus (Boston Univ.).
• NASA SUPERball v2 — SunSpiral 2015 NASA tech report or NTRTsim JSON for the per-node payload-cable routing.
• Tibert/Pellegrino mast — Sultan & Skelton (2003) or Bel Hadj Ali et al. (2010) for the equilibrium-manifold deployment trajectory (only static topology reproduced here).
• Knight et al. antenna (US 6,441,801 B1) — Figs. 2–4 of the patent for exact strut/tie ratios + screw-motion deployment schedule.
• Bistable double-prism — Intrigila et al. Add. Manuf. 57:102946 (2022), Figs. 6–9, for hinge cross-sections + triggering force.
• Liu et al. cuboctahedron tessellation — J. Mech. Phys. Solids 131:147–166 (2019) supplementary material for the full 13-strut / 96-cable / 12-prestress-state form-finding (the STL committed is a simplified single-block representation).

If you can grab any of those PDFs (or contact someone), I can refine the corresponding STL in a follow-up. CodeQL is clean; addressed Code Review nits (explained 0.25 curvature scalar, documented the T3 twist angle in bistable_double_prism, added the Google Patents URL) in fd32935.

[sgbaird-yolo]

all 7 remaining design families

@copilot are there any other major design families we're missing? Send a follow-up edison query

[Copilot]

all 7 remaining design families

@copilot are there any other major design families we're missing? Send a follow-up edison query

Submitted Edison LITERATURE_HIGH follow-up task 6226a551-b46a-49b4-936a-bca600cd8d30 and fetched it in-session (~32 min). Full survey (~38 KB md, 68 KB json, 9 KB extracted refs) committed in 119d9c6 alongside the submission script:

• edison-trajectories/2026-05-12-tensegrity-design-gaps-6226a551-….md
• …-references.md, …json
• scripts/edison/submit_tensegrity_gaps_followup.py

18 missing families identified, ranked by usefulness to the PETG+TPU/H2D impact-absorber project. Top picks:

1. Snelson X-module (planar crossed-strut weave; flat-printable; Motro / Cowcher 2015) — flagged as "the single most buildable next addition"
2. Pajunen 2019 3D-printable truncated-octa impact cell (10.1016/j.matdes.2019.107966) — reusable under impacts, low ρ_rel
3. Oster 2021 reentrant 3-periodic auxetic tensegrity (Sci. Adv., 10.1126/sciadv.abj6737) — negative Poisson ratio cushioning
4. Rhode-Barbarigos pentagonal tensegrity-ring module (15/30/15, 10.1016/j.engstruct.2009.12.042) — deployable, annular crutch-collar topology
   5–6. Pugh diamond / zig-zag patterns (Pugh 1976) — canonical-completeness, anisotropic crush response
5. Tensegrity torus (Murakami 2001, 10.1016/S0020-7683(00)00233-X) — donut/crutch-tip form
6. Hanaor double-layer tensegrity grid (1991/1993) — multilayer pads
7. Charalambides & Liapi 2017 square-base double-layer unit
8. Levy / Suspen-dome family (Olofin & Liu 2017; Chen 2015) — canonical-completeness
   11–12. DNA tensegrities (Liedl 2010 prism; Seeman/Kong 2023 triangle crystal) — molecular-scale completeness
9. US 2024/0351370 A1 6-bar icosahedral tensegrity wheel — patent-family
10. Schenk & Guest 2014 zero-stiffness / bistable tensegrity arch-beams
11. Ding 2025 D-bar / class-k auxetic tensegrity metamaterials (10.1088/1361-665X/add22d)
12. Sabouni-Zawadzka 2025 AM auxetic tensegrity-like lattice (10.1016/j.matdes.2025.114513)
13. Hao 2026 clustered multistable tensegrity (10.1088/1361-665X/ae3ff8)
14. Simmons 2026 star-shaped tensegrity-inspired impact lattice (10.1088/2631-8695/ae3530)

Survey confirms our 13 already cover the highest-impact buildable families; the gap list is dominated by (a) Snelson/Pugh canonical-completeness items and (b) 2024–2026 auxetic/multistable metamaterial papers. If you want, in a follow-up I can extend generate_stl.py with #1, #3, #4 (the three with explicit-enough geometry to do as parametric STLs without needing supplementary materials). For #2/#15/#16/#17/#18 I'd want the paper PDFs first — let me know and I can list which specific figures/tables are needed.

[sgbaird-alt]

@me-madsen @achris0520 @ctrhjk could one of you try to get the missing papers mentioned in https://github.com/vertical-cloud-lab/tensegrity-optimization/blob/copilot/fetch-designs-for-tensegrity-structures/models/README.md#source-materials-needed-for-the-remaining-gap-followup-families ? Don't worry if you don't get all of them (e.g., bad link provided, BYU doesn't have access, etc.). You can send to me via slack (can upload to tensegrity channel)

[ctrhjk]

Found the following references/resources:

• "Floating fabric over Georgia Dome", Civ. Eng. ASCE 61(11):34-37, 1991
  -> BYU Library has a copy, and I requested a PDF scan of the paper.

• Kim, K., Agogino, A. K., Toghyan, A., Moon, D., Taneja, L., Agogino, A. M., "Robust learning of tensegrity robot control for locomotion through form-finding", IROS 2015
  DOI: https://doi.org/10.1109/IROS.2015.7354204

[me-madsen]

@me-madsen maybe we could try printing the other two T4 and icosahedron similar to #35

A test print for the T4 is underway (PLA) with the same file for which a TPU + PLA test print is underway. See vertical-cloud-lab/byu-vcl#82 (comment)

Waiting until after to try the icosahedron as I would like to try and optimize the supports. Automatic supports for it looked far too messy.

[ctrhjk]

"Floating fabric over Georgia Dome", Civ. Eng. ASCE 61(11):34-37, 1991
This is the link that contains the PDF of this article

https://verticalcloudlabbyu.slack.com/archives/C0B2MFR5V3L/p1778691467813409