8/78

TILER Tiles space periodically. 3 copies per repeating block, on a lattice of index 24. No box through volume 96 was found first.

shape tiling

drag to orbit, scroll to zoom

cells: 8, bounding box 1×2×6
symmetry order: 1
chiral: no, its own mirror image
record: data/8/78/shape.json

Stages

stage	outcome	at
box	exhausted	96
torus	certified	24

Downloads

model.stl the shape, printable
tiling.obj a chunk of the tiling, one colour per copy
shape.json the record

The record, as stored

{
  "id": "8/78",
  "n": 8,
  "cells": [[0, 0, 0], [0, 0, 1], [0, 0, 2], [0, 0, 3], [0, 0, 4], [0, 1, 0], [0, 1, 4], [0, 1, 5]],
  "symmetry_order": 1,
  "chiral": false,
  "mirror_id": "8/78",
  "verdict": "tiler",
  "tiles_rotations_only": true,
  "tiles_with_reflections": true,
  "certificate": {
    "lattice": [[8, 0, 0], [1, 3, 0], [3, 2, 1]],
    "placements": [
      { "offset": [7, 2, 0], "rotation": 5 },
      { "offset": [7, 1, 0], "rotation": 16 },
      { "offset": [7, 2, 0], "rotation": 23 }
    ],
    "type": "torus"
  },
  "heesch": null,
  "budgets": { "box_max_volume": 96, "torus_max_index": 48 },
  "credits": { "prior_art": null, "solved_by": "polycube-census v0.1.0", "verified_by": null },
  "stages": [
    { "outcome": "exhausted", "stage": "box", "volume": 96 },
    { "index": 24, "outcome": "certified", "stage": "torus" }
  ]
}