9/24830

OPEN Survived every test within its budgets. No box tiling through volume 96. No periodic tiling through lattice index 72. Wraps itself 2 times, with a verified witness.

shape corona 1 corona 2

drag to orbit, scroll to zoom

cells: 9, bounding box 4×3×2
symmetry order: 1
chiral: yes, twin 9/24025
Heesch number: ≥ 2
record: data/9/24830/shape.json

Stages

stage	outcome	at
box	exhausted	96
torus	exhausted	72
corona	witnessed	2

Downloads

model.stl the shape, printable
corona1.json the depth-1 witness, as placements
corona2.json the depth-2 witness, as placements
shape.json the record

The record, as stored

{
  "id": "9/24830",
  "n": 9,
  "cells": [[0, 0, 0], [0, 0, 1], [0, 1, 0], [1, 1, 0], [1, 1, 1], [1, 2, 1], [2, 1, 0], [2, 2, 0], [3, 1, 0]],
  "symmetry_order": 1,
  "chiral": true,
  "mirror_id": "9/24025",
  "verdict": "open",
  "tiles_rotations_only": null,
  "tiles_with_reflections": null,
  "certificate": null,
  "heesch": null,
  "budgets": { "box_max_volume": 96, "torus_max_index": 72 },
  "credits": {
    "prior_art": null,
    "solved_by": "polycube-census v0.1.0 (corona witnesses mirrored from 9/24025)",
    "verified_by": null
  },
  "reached": { "corona_sat": 2 },
  "stages": [
    { "outcome": "exhausted", "stage": "box", "volume": 96 },
    { "index": 72, "outcome": "exhausted", "stage": "torus" },
    { "depth": 2, "outcome": "witnessed", "stage": "corona" }
  ]
}