{
  "meta": {
    "schema_version": 2,
    "range": {
      "minimum_colours": 1,
      "maximum_colours": 6
    },
    "manifest_source": "color-forward-manifest.json",
    "manifest_sha256": "e69cae9f528b264f240bd97b0eec14615ad83c186afcdd5284d719f165c1a4ad",
    "source_catalog": {
      "description": "Pinned 275-group catalog snapshot",
      "path": "docs/data/catalog.json",
      "sha256": "040eebe747815557014c1dbf1d4265d204aaae35c110595f2a15b94ee7f68ca0",
      "total_groups": 275,
      "forward_groups": 68
    },
    "label_conventions": {
      "primary": "Conway orbifold notation",
      "orbifold_field": "orbifold",
      "traceability": "wallpaper_group retains the source catalog's International short (Hermann–Mauguin) code"
    },
    "definitions": {
      "wieting_all_transitive": "Plane-affine classes of all index-N colour stabilizers.",
      "regular_cyclic_kernels": "Plane-affine classes of normal index-N kernels with quotient C_N.",
      "forward_catalog_canonical_clock_order": "Forward representatives in the 275-group source catalog whose displayed temporal offsets generate a cyclic group of exact order N."
    },
    "warning": "The three columns use different equivalence relations. The forward column is a canonical-representative statistic, not the number of all N-colourings of forward film groups.",
    "sources": [
      {
        "label": "Wieting Table 11 totals (OEIS A307293)",
        "url": "https://oeis.org/A307293"
      },
      {
        "label": "Pinned Senechal-Wieting subgroup reconstruction",
        "url": "https://github.com/yaroslavvb/wieting-subgroups/tree/dc192b34f206e6fd8e0533c6a25ab89a6055b9ff"
      },
      {
        "label": "Jarratt-Schwarzenberger coloured plane groups",
        "url": "https://doi.org/10.1107/S0567739480001866"
      }
    ]
  },
  "summary": [
    {
      "colours": 1,
      "wieting_all_transitive": 17,
      "regular_cyclic_kernels": 17,
      "forward_catalog_canonical_clock_order": 17
    },
    {
      "colours": 2,
      "wieting_all_transitive": 46,
      "regular_cyclic_kernels": 46,
      "forward_catalog_canonical_clock_order": 36
    },
    {
      "colours": 3,
      "wieting_all_transitive": 23,
      "regular_cyclic_kernels": 8,
      "forward_catalog_canonical_clock_order": 6
    },
    {
      "colours": 4,
      "wieting_all_transitive": 96,
      "regular_cyclic_kernels": 13,
      "forward_catalog_canonical_clock_order": 6
    },
    {
      "colours": 5,
      "wieting_all_transitive": 14,
      "regular_cyclic_kernels": 4,
      "forward_catalog_canonical_clock_order": 0
    },
    {
      "colours": 6,
      "wieting_all_transitive": 90,
      "regular_cyclic_kernels": 13,
      "forward_catalog_canonical_clock_order": 3
    }
  ],
  "by_wallpaper": [
    {
      "orbifold": "◦",
      "wallpaper_group": "p1",
      "regular_cyclic": {
        "1": 1,
        "2": 1,
        "3": 1,
        "4": 1,
        "5": 1,
        "6": 1
      },
      "forward_catalog": {
        "1": 1,
        "2": 0,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 1
    },
    {
      "orbifold": "2222",
      "wallpaper_group": "p2",
      "regular_cyclic": {
        "1": 1,
        "2": 2,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_catalog": {
        "1": 1,
        "2": 2,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 3
    },
    {
      "orbifold": "**",
      "wallpaper_group": "pm",
      "regular_cyclic": {
        "1": 1,
        "2": 5,
        "3": 1,
        "4": 3,
        "5": 1,
        "6": 5
      },
      "forward_catalog": {
        "1": 1,
        "2": 0,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 1
    },
    {
      "orbifold": "××",
      "wallpaper_group": "pg",
      "regular_cyclic": {
        "1": 1,
        "2": 2,
        "3": 1,
        "4": 2,
        "5": 1,
        "6": 2
      },
      "forward_catalog": {
        "1": 1,
        "2": 0,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 1
    },
    {
      "orbifold": "*×",
      "wallpaper_group": "cm",
      "regular_cyclic": {
        "1": 1,
        "2": 3,
        "3": 1,
        "4": 2,
        "5": 1,
        "6": 3
      },
      "forward_catalog": {
        "1": 1,
        "2": 1,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 2
    },
    {
      "orbifold": "*2222",
      "wallpaper_group": "pmm",
      "regular_cyclic": {
        "1": 1,
        "2": 5,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_catalog": {
        "1": 1,
        "2": 5,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 6
    },
    {
      "orbifold": "22*",
      "wallpaper_group": "pmg",
      "regular_cyclic": {
        "1": 1,
        "2": 5,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_catalog": {
        "1": 1,
        "2": 5,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 6
    },
    {
      "orbifold": "22×",
      "wallpaper_group": "pgg",
      "regular_cyclic": {
        "1": 1,
        "2": 2,
        "3": 0,
        "4": 1,
        "5": 0,
        "6": 0
      },
      "forward_catalog": {
        "1": 1,
        "2": 2,
        "3": 0,
        "4": 1,
        "5": 0,
        "6": 0
      },
      "forward_total": 4
    },
    {
      "orbifold": "2*22",
      "wallpaper_group": "cmm",
      "regular_cyclic": {
        "1": 1,
        "2": 5,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_catalog": {
        "1": 1,
        "2": 5,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 6
    },
    {
      "orbifold": "442",
      "wallpaper_group": "p4",
      "regular_cyclic": {
        "1": 1,
        "2": 2,
        "3": 0,
        "4": 2,
        "5": 0,
        "6": 0
      },
      "forward_catalog": {
        "1": 1,
        "2": 2,
        "3": 0,
        "4": 3,
        "5": 0,
        "6": 0
      },
      "forward_total": 6
    },
    {
      "orbifold": "*442",
      "wallpaper_group": "p4m",
      "regular_cyclic": {
        "1": 1,
        "2": 5,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_catalog": {
        "1": 1,
        "2": 5,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 6
    },
    {
      "orbifold": "4*2",
      "wallpaper_group": "p4g",
      "regular_cyclic": {
        "1": 1,
        "2": 3,
        "3": 0,
        "4": 2,
        "5": 0,
        "6": 0
      },
      "forward_catalog": {
        "1": 1,
        "2": 3,
        "3": 0,
        "4": 2,
        "5": 0,
        "6": 0
      },
      "forward_total": 6
    },
    {
      "orbifold": "333",
      "wallpaper_group": "p3",
      "regular_cyclic": {
        "1": 1,
        "2": 0,
        "3": 2,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_catalog": {
        "1": 1,
        "2": 0,
        "3": 3,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 4
    },
    {
      "orbifold": "*333",
      "wallpaper_group": "p3m1",
      "regular_cyclic": {
        "1": 1,
        "2": 1,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_catalog": {
        "1": 1,
        "2": 1,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 2
    },
    {
      "orbifold": "3*3",
      "wallpaper_group": "p31m",
      "regular_cyclic": {
        "1": 1,
        "2": 1,
        "3": 1,
        "4": 0,
        "5": 0,
        "6": 1
      },
      "forward_catalog": {
        "1": 1,
        "2": 1,
        "3": 1,
        "4": 0,
        "5": 0,
        "6": 1
      },
      "forward_total": 4
    },
    {
      "orbifold": "632",
      "wallpaper_group": "p6",
      "regular_cyclic": {
        "1": 1,
        "2": 1,
        "3": 1,
        "4": 0,
        "5": 0,
        "6": 1
      },
      "forward_catalog": {
        "1": 1,
        "2": 1,
        "3": 2,
        "4": 0,
        "5": 0,
        "6": 2
      },
      "forward_total": 6
    },
    {
      "orbifold": "*632",
      "wallpaper_group": "p6m",
      "regular_cyclic": {
        "1": 1,
        "2": 3,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_catalog": {
        "1": 1,
        "2": 3,
        "3": 0,
        "4": 0,
        "5": 0,
        "6": 0
      },
      "forward_total": 4
    }
  ],
  "forward_groups_by_order": {
    "1": [
      {
        "id": "g1",
        "symbol": "o",
        "base": "p1",
        "orbifold": "◦",
        "canonical_clock_order": 1
      },
      {
        "id": "g5",
        "symbol": "2222",
        "base": "p2",
        "orbifold": "2222",
        "canonical_clock_order": 1
      },
      {
        "id": "g10",
        "symbol": "**",
        "base": "pm",
        "orbifold": "**",
        "canonical_clock_order": 1
      },
      {
        "id": "g11",
        "symbol": "××",
        "base": "pg",
        "orbifold": "××",
        "canonical_clock_order": 1
      },
      {
        "id": "g8",
        "symbol": "*×",
        "base": "cm",
        "orbifold": "*×",
        "canonical_clock_order": 1
      },
      {
        "id": "g54",
        "symbol": "*2222",
        "base": "pmm",
        "orbifold": "*2222",
        "canonical_clock_order": 1
      },
      {
        "id": "g56",
        "symbol": "22*",
        "base": "pmg",
        "orbifold": "22*",
        "canonical_clock_order": 1
      },
      {
        "id": "g58",
        "symbol": "22×",
        "base": "pgg",
        "orbifold": "22×",
        "canonical_clock_order": 1
      },
      {
        "id": "g68",
        "symbol": "2*22",
        "base": "cmm",
        "orbifold": "2*22",
        "canonical_clock_order": 1
      },
      {
        "id": "g94",
        "symbol": "442",
        "base": "p4",
        "orbifold": "442",
        "canonical_clock_order": 1
      },
      {
        "id": "g128",
        "symbol": "*442",
        "base": "p4m",
        "orbifold": "*442",
        "canonical_clock_order": 1
      },
      {
        "id": "g132",
        "symbol": "4*2",
        "base": "p4g",
        "orbifold": "4*2",
        "canonical_clock_order": 1
      },
      {
        "id": "g224",
        "symbol": "333",
        "base": "p3",
        "orbifold": "333",
        "canonical_clock_order": 1
      },
      {
        "id": "g230",
        "symbol": "*333",
        "base": "p3m1",
        "orbifold": "*333",
        "canonical_clock_order": 1
      },
      {
        "id": "g232",
        "symbol": "3*3",
        "base": "p31m",
        "orbifold": "3*3",
        "canonical_clock_order": 1
      },
      {
        "id": "g243",
        "symbol": "632",
        "base": "p6",
        "orbifold": "632",
        "canonical_clock_order": 1
      },
      {
        "id": "g268",
        "symbol": "*632",
        "base": "p6m",
        "orbifold": "*632",
        "canonical_clock_order": 1
      }
    ],
    "2": [
      {
        "id": "g6",
        "symbol": "2₁2₁2₁2₁",
        "base": "p2",
        "orbifold": "2222",
        "canonical_clock_order": 2
      },
      {
        "id": "g7",
        "symbol": "c222₁2₁",
        "base": "p2",
        "orbifold": "2222",
        "canonical_clock_order": 2
      },
      {
        "id": "g9",
        "symbol": "~*×½",
        "base": "cm",
        "orbifold": "*×",
        "canonical_clock_order": 2
      },
      {
        "id": "g55",
        "symbol": "*~2~2~2~2",
        "base": "pmm",
        "orbifold": "*2222",
        "canonical_clock_order": 2
      },
      {
        "id": "g60",
        "symbol": "*2₁~2₁2₁~2₁",
        "base": "pmm",
        "orbifold": "*2222",
        "canonical_clock_order": 2
      },
      {
        "id": "g64",
        "symbol": "c*222₁2₁ᵃ",
        "base": "pmm",
        "orbifold": "*2222",
        "canonical_clock_order": 2
      },
      {
        "id": "g65",
        "symbol": "c*222₁2₁ᵇ",
        "base": "pmm",
        "orbifold": "*2222",
        "canonical_clock_order": 2
      },
      {
        "id": "g74",
        "symbol": "c*22₁22₁",
        "base": "pmm",
        "orbifold": "*2222",
        "canonical_clock_order": 2
      },
      {
        "id": "g57",
        "symbol": "22~*",
        "base": "pmg",
        "orbifold": "22*",
        "canonical_clock_order": 2
      },
      {
        "id": "g61",
        "symbol": "2₁2₁~*",
        "base": "pmg",
        "orbifold": "22*",
        "canonical_clock_order": 2
      },
      {
        "id": "g62",
        "symbol": "2₁2₁*",
        "base": "pmg",
        "orbifold": "22*",
        "canonical_clock_order": 2
      },
      {
        "id": "g66",
        "symbol": "c22₁*ᵃ",
        "base": "pmg",
        "orbifold": "22*",
        "canonical_clock_order": 2
      },
      {
        "id": "g67",
        "symbol": "c22₁*ᵇ",
        "base": "pmg",
        "orbifold": "22*",
        "canonical_clock_order": 2
      },
      {
        "id": "g59",
        "symbol": "22×½",
        "base": "pgg",
        "orbifold": "22×",
        "canonical_clock_order": 2
      },
      {
        "id": "g63",
        "symbol": "2₁2₁×",
        "base": "pgg",
        "orbifold": "22×",
        "canonical_clock_order": 2
      },
      {
        "id": "g69",
        "symbol": "2*~2~2",
        "base": "cmm",
        "orbifold": "2*22",
        "canonical_clock_order": 2
      },
      {
        "id": "g70",
        "symbol": "2₁*2₁~2₁",
        "base": "cmm",
        "orbifold": "2*22",
        "canonical_clock_order": 2
      },
      {
        "id": "g71",
        "symbol": "c2₁*22ᵃ",
        "base": "cmm",
        "orbifold": "2*22",
        "canonical_clock_order": 2
      },
      {
        "id": "g72",
        "symbol": "c2₁*22ᵇ",
        "base": "cmm",
        "orbifold": "2*22",
        "canonical_clock_order": 2
      },
      {
        "id": "g73",
        "symbol": "c2*2₁2₁",
        "base": "cmm",
        "orbifold": "2*22",
        "canonical_clock_order": 2
      },
      {
        "id": "g95",
        "symbol": "4₂4₂2",
        "base": "p4",
        "orbifold": "442",
        "canonical_clock_order": 2
      },
      {
        "id": "g98",
        "symbol": "c44₂2₁",
        "base": "p4",
        "orbifold": "442",
        "canonical_clock_order": 2
      },
      {
        "id": "g129",
        "symbol": "*4₂~4₂2",
        "base": "p4m",
        "orbifold": "*442",
        "canonical_clock_order": 2
      },
      {
        "id": "g130",
        "symbol": "*~4₂4₂~2",
        "base": "p4m",
        "orbifold": "*442",
        "canonical_clock_order": 2
      },
      {
        "id": "g131",
        "symbol": "*~4~4~2",
        "base": "p4m",
        "orbifold": "*442",
        "canonical_clock_order": 2
      },
      {
        "id": "g136",
        "symbol": "c*44₂2₁ᵃ",
        "base": "p4m",
        "orbifold": "*442",
        "canonical_clock_order": 2
      },
      {
        "id": "g138",
        "symbol": "c*44₂2₁ᵇ",
        "base": "p4m",
        "orbifold": "*442",
        "canonical_clock_order": 2
      },
      {
        "id": "g133",
        "symbol": "4₂*~2",
        "base": "p4g",
        "orbifold": "4*2",
        "canonical_clock_order": 2
      },
      {
        "id": "g134",
        "symbol": "4₂*2",
        "base": "p4g",
        "orbifold": "4*2",
        "canonical_clock_order": 2
      },
      {
        "id": "g135",
        "symbol": "4*~2",
        "base": "p4g",
        "orbifold": "4*2",
        "canonical_clock_order": 2
      },
      {
        "id": "g231",
        "symbol": "*~3~3~3",
        "base": "p3m1",
        "orbifold": "*333",
        "canonical_clock_order": 2
      },
      {
        "id": "g233",
        "symbol": "3*~3",
        "base": "p31m",
        "orbifold": "3*3",
        "canonical_clock_order": 2
      },
      {
        "id": "g246",
        "symbol": "6₃32₁",
        "base": "p6",
        "orbifold": "632",
        "canonical_clock_order": 2
      },
      {
        "id": "g269",
        "symbol": "*6₃~3~2₁",
        "base": "p6m",
        "orbifold": "*632",
        "canonical_clock_order": 2
      },
      {
        "id": "g270",
        "symbol": "*~6~3~2",
        "base": "p6m",
        "orbifold": "*632",
        "canonical_clock_order": 2
      },
      {
        "id": "g271",
        "symbol": "*~6₃32₁",
        "base": "p6m",
        "orbifold": "*632",
        "canonical_clock_order": 2
      }
    ],
    "3": [
      {
        "id": "g225",
        "symbol": "3₂3₂3₂",
        "base": "p3",
        "orbifold": "333",
        "canonical_clock_order": 3
      },
      {
        "id": "g226",
        "symbol": "3₁3₁3₁",
        "base": "p3",
        "orbifold": "333",
        "canonical_clock_order": 3
      },
      {
        "id": "g227",
        "symbol": "r33₁3₂",
        "base": "p3",
        "orbifold": "333",
        "canonical_clock_order": 3
      },
      {
        "id": "g234",
        "symbol": "r3₂*3",
        "base": "p31m",
        "orbifold": "3*3",
        "canonical_clock_order": 3
      },
      {
        "id": "g244",
        "symbol": "6₂3₂2",
        "base": "p6",
        "orbifold": "632",
        "canonical_clock_order": 3
      },
      {
        "id": "g245",
        "symbol": "6₄3₁2",
        "base": "p6",
        "orbifold": "632",
        "canonical_clock_order": 3
      }
    ],
    "4": [
      {
        "id": "g75",
        "symbol": "c22₁×¼",
        "base": "pgg",
        "orbifold": "22×",
        "canonical_clock_order": 4
      },
      {
        "id": "g96",
        "symbol": "4₁4₁2₁",
        "base": "p4",
        "orbifold": "442",
        "canonical_clock_order": 4
      },
      {
        "id": "g97",
        "symbol": "4₃4₃2₁",
        "base": "p4",
        "orbifold": "442",
        "canonical_clock_order": 4
      },
      {
        "id": "g99",
        "symbol": "c4₁4₃2",
        "base": "p4",
        "orbifold": "442",
        "canonical_clock_order": 4
      },
      {
        "id": "g137",
        "symbol": "c4₃*2",
        "base": "p4g",
        "orbifold": "4*2",
        "canonical_clock_order": 4
      },
      {
        "id": "g139",
        "symbol": "c4₁*2",
        "base": "p4g",
        "orbifold": "4*2",
        "canonical_clock_order": 4
      }
    ],
    "5": [],
    "6": [
      {
        "id": "g235",
        "symbol": "r3₂*~3",
        "base": "p31m",
        "orbifold": "3*3",
        "canonical_clock_order": 6
      },
      {
        "id": "g247",
        "symbol": "6₅3₂2₁",
        "base": "p6",
        "orbifold": "632",
        "canonical_clock_order": 6
      },
      {
        "id": "g248",
        "symbol": "6₁3₁2₁",
        "base": "p6",
        "orbifold": "632",
        "canonical_clock_order": 6
      }
    ]
  }
}