{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "WC4QAGSMWR"
    }
  ],
  "body": "\n## Summary\n\nA penny graph is the contact graph of a set of equal coins lying flat on a table without overlapping.\nEach coin is a vertex, and two coins are joined when they touch.\nPenny graphs are [[planar graphs|0NC9R64TXP]] with maximum degree at most $6$, and they are a test case for questions about unit distances and [[circle packings|S360JBEYKD]].\n\n## Explanations\n\n### L1 human\n\nLay some identical coins on a table so that none overlap.\nDraw a dot at the centre of each coin and a line between the centres of two coins that touch.\nThe drawing is a penny graph.\nSix coins around a central coin, all touching it and their neighbours, give a hexagon with its centre, a penny graph with $7$ vertices and $12$ edges.\nNo coin can touch more than six others, since a seventh would not fit around it.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "05C62",
      "52C15",
      "52C10"
    ],
    "name": "Penny graph",
    "same_as": {
      "wikidata": "Q30592245",
      "wikipedia": "Penny graph"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Penny_graph"
      }
    ],
    "specializes": [
      "0NC9R64TXP"
    ],
    "tag": "6DG5BBQPRA"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/6DG5BBQPRA/",
  "links": [
    {
      "field": "specializes",
      "target": "0NC9R64TXP"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/6DG5BBQPRA.md",
  "msc": [
    "05C62",
    "52C15",
    "52C10"
  ],
  "name": "Penny graph",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/6DG/6DG5BBQPRA.md",
  "status": null,
  "tag": "6DG5BBQPRA",
  "uri": "m2://6DG5BBQPRA",
  "url": "https://tamnd.github.io/math2/wiki/penny-graph/",
  "writing": {
    "tag": "6DG5BBQPRA",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}