---
id: "2026-10-05-rhombicosidodecahedron-not-rupert-claude"
url: "https://postcutoff.com/e/2026-10-05-rhombicosidodecahedron-not-rupert-claude/"
as_of: "2026-10-14T07:26:00+02:00"
date: "2026-10-05"
date_precision: day
category: science
importance: 3
confidence: medium
status: [Awaiting review]
verification: Expert-checked
sources: 6
editor: human editor
human_review: null
version: null
---

As of: 2026-10-14 07:26 CEST.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2026-10-05-rhombicosidodecahedron-not-rupert-claude/

# Teen's Claude-coded proof claims rhombicosidodecahedron is not Rupert

Full title: A 15-year-old's computer-assisted preprint, coded with Claude, claims the rhombicosidodecahedron is not Rupert (Steininger–Yurkevich conjecture)

On Oct 5, 2026 Gihyo Jung, described by Korean media as a 15-year-old ninth grader, posted "The rhombicosidodecahedron is not Rupert" on Zenodo with code on GitHub: a computer-assisted proof that this Archimedean solid cannot pass through a hole in a congruent copy of itself, settling a conjecture of Steininger and Yurkevich. He says Claude wrote the proof code. Not yet peer-reviewed or independently checked.

## Key facts
- Preprint: Gihyo Jung, 'The rhombicosidodecahedron is not Rupert', Zenodo 10.5281/zenodo.23159625, Oct 5, 2026 (about 7.8k views by Oct 14); code at github.com/swiri0921-bit/rhombicosidodecahedron-not-rupert
- Abstract: settles a conjecture of Steininger and Yurkevich, who built the first convex polyhedron without the Rupert property (the 'Noperthedron', arXiv 2508.18475, 2025). Because of the solid's symmetry, the standard subdivision method does not work alone, so the paper adds three new local certificates
- Method (README): implements Steininger–Yurkevich's global and local theorems; outward-rounded interval arithmetic with rigorous sin/cos; exact identities in Q(√5); LP (HiGHS) used only to find witnesses, all re-verified; cell cover of 211,680 cells (1.23e7 leaves) with 0 failures; a second implementation in exact rational arithmetic. About 38 hours of computation on a laptop
- Background: Steininger and Yurkevich conjectured (2021) that the rhombicosidodecahedron is not Rupert; their 2025 Noperthedron methods did not suffice for it. Benjamin Grimmer (Johns Hopkins) had told Quanta that two weeks of computer search on it 'just seems to resist any attempt'
- AI use (press, not in the Zenodo record or README): Jung told JoongAng Ilbo he used Claude 'to generate code for solving a difficult mathematical problem and then reviewing the results'; Korea Daily says he also used AI to check the proof and help write the paper. His Reddit post topped a Claude coding forum on Oct 10
- Jung says he chose the topic without an adviser, admits he cannot independently verify every detail, and says another study reached the same conclusion by a different method around the same time (not named; not found)
- Korean experts (JoongAng): Oum Sang-il (IBS Discrete Mathematics Group): posting 'establishes a public record of when it was released' but 'does not guarantee the validity of its contents'; Seo In-suk (SNU): the author must understand all details and answer questions; Choi Kyu-dong (UNIST): lack of training and a paper's value 'can be distinct'

## What happened

A convex polyhedron is "Rupert" if a straight tunnel can be cut through it large enough for a congruent copy to pass through
(Prince Rupert's cube puzzle, c. 1693). For decades every convex polyhedron tested turned out to be Rupert, until Jakob
Steininger and Sergey Yurkevich proved in 2025 that a purpose-built polyhedron, the Noperthedron, is not. They had earlier
conjectured that the rhombicosidodecahedron (20 triangles, 30 squares, 12 pentagons) is not Rupert either, but their methods did
not settle it.

On Oct 5, 2026 Gihyo Jung posted a computer-assisted proof of that conjecture on Zenodo, with a GitHub repository of certificates
and two independent checkers. Korean newspapers (Korea Daily, Oct 13; JoongAng Ilbo, Oct 14) reported that he is a ninth grader
and that Claude wrote the code. Neither the Zenodo record nor the README contains an AI disclosure; the AI role is known only from
his interviews.

## Why it matters

If it holds, it is the second named non-Rupert polyhedron and the first Archimedean solid shown not to be Rupert, from an author
with no formal training working with a coding agent. The Korean debate centres on authorship: whether a paper counts if its author
cannot check every step himself.

## What is disputed or not yet verified

- Verification: unverified claim (computer-assisted certificates published with code; no peer review or independent check reported as of Oct 14)

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): 158 days after its cutoff
- Claude Opus 5.5 (training cutoff June 2026): 97 days after its cutoff
- Gemini 4 Argon (training cutoff March 2026): 188 days after its cutoff
- Grok 4.7 (training cutoff May 2026): 127 days after its cutoff

## Sources

1. [Zenodo: G. Jung, The rhombicosidodecahedron is not Rupert (Oct 5, 2026)](https://zenodo.org/records/23159625) (zenodo.org, paper)
2. [GitHub: proof code and certificates](https://github.com/swiri0921-bit/rhombicosidodecahedron-not-rupert) (github.com, code)
3. [Steininger & Yurkevich: A convex polyhedron without Rupert's property (arXiv 2508.18475)](https://arxiv.org/abs/2508.18475) (arxiv.org, paper)
4. [Korea JoongAng Daily: 15-year-old claims AI helped crack 300-year-old math puzzle (Oct 14)](https://www.koreajoongangdaily.com/korea/15yearold-claims-ai-helped-crack-300yearold-math-puzzle/12919724) (koreajoongangdaily.com, press)
5. [Korea Daily: Rupert's Hypothesis — South Korean middle schooler tackles 300-year-old math problem using AI (Oct 13)](https://en.koreadaily.com/ruperts-hypothesis-ai-math-middle-schooler/) (en.koreadaily.com, press)
6. [Quanta: First shape found that can't pass through itself (Oct 2025)](https://www.quantamagazine.org/first-shape-found-that-cant-pass-through-itself-20251024/) (quantamagazine.org, press)

## Changes

- 2026-10-14 (filed): Created (Google News: Korea Daily and JoongAng Daily); verification status pending

## Related

- 2026-10-13: [October 2026: the arXiv stream of conjectures settled with disclosed AI help continues](https://postcutoff.com/e/2026-10-13-ai-assisted-results-october-2026/index.md)
- 2026-09-30: [Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help](https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/index.md)