---
tag: HTJ03RFKFH
kind: concept
name: Honeycomb
msc: [52C22, 51M20, 05B45]
specializes: [GKJK293DXS]
sources:
  - url: https://en.wikipedia.org/wiki/Honeycomb_(geometry)
same_as:
  wikidata: Q1189295
  wikipedia: Honeycomb (geometry)
---

## Summary

A honeycomb is a filling of three-dimensional space, or of a higher-dimensional space, by [[polyhedra|0325SGSJAR]] or polytopes without gaps or overlaps.
It is the analogue in space of a [[tessellation|GKJK293DXS]] of the plane by polygons.
Honeycombs occur in crystallography, in [[sphere packing|HF32CBN5MA]] and in the study of regular and uniform polytopes.

## Explanations

### L1 human

Stack equal cubes like boxes in a warehouse, filling space completely in every direction.
The result, the cubic honeycomb, is the simplest honeycomb.
The cells may also be other solids, such as truncated octahedra or hexagonal prisms.
Regular tetrahedra alone cannot fill space: their dihedral angle of about $70.5^\circ$ does not divide $360^\circ$.