HALOWERKDatenvertragswerk
orientable rotation system genus family
For a fully captured CONNECTED simple undirected graph on1..4 labels0..n-1, generate EVERY cyclic neighbor order at every vertex. Fix the smallest neighbor first in each cycle; retain mirrored orders and original labels, no graphisomorphism/reflection quotient. Return canonical edge_order, all systems{rotations,faces,genus}, count and genus_histogram[genus0count,genus1count]. Systems sort lexicographically by vertex-indexed neighbororders. Dart2i follows edge_order[i] lower-to-higher;.
POST https://datenvertrag.halowerk.com/v1/orientable-rotation-system-genus-familyEingaben
| Feld | Typ | Pflicht | Beschreibung |
|---|---|---|---|
| n | Siehe Schema | Ja | |
| edges | Siehe Schema | Ja | |
| claim | Siehe Schema | Ja |
Vollständiges Eingabeschema anzeigen
{
"type": "object",
"properties": {
"n": {
"anyOf": [
{
"type": "integer",
"minimum": 1,
"maximum": 4
},
{
"type": "null"
}
]
},
"edges": {
"anyOf": [
{
"type": "array",
"items": {
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 2,
"maxItems": 2
},
"minItems": 0,
"maxItems": 6
},
{
"type": "null"
}
]
},
"claim": {
"anyOf": [
{
"type": "object",
"properties": {
"edge_order": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 2,
"maxItems": 2
},
"minItems": 0,
"maxItems": 6
},
"systems": {
"type": "array",
"items": {
"type": "object",
"properties": {
"rotations": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 3
},
"minItems": 0,
"maxItems": 3
},
"minItems": 1,
"maxItems": 4
},
"faces": {
"type": "array",
"items": {
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 11
},
"minItems": 0,
"maxItems": 12
},
"minItems": 1,
"maxItems": 12
},
"genus": {
"type": "integer",
"minimum": 0,
"maximum": 1
}
},
"required": [
"rotations",
"faces",
"genus"
],
"additionalProperties": false
},
"minItems": 1,
"maxItems": 16
},
"count": {
"type": "integer",
"minimum": 1,
"maximum": 16
},
"genus_histogram": {
"type": "array",
"items": {
"type": "integer",
"minimum": 0,
"maximum": 16
},
"minItems": 2,
"maxItems": 2
}
},
"required": [
"edge_order",
"systems",
"count",
"genus_histogram"
],
"additionalProperties": false
},
{
"type": "null"
}
]
}
},
"required": [
"n",
"edges",
"claim"
],
"additionalProperties": false
}Veröffentlichtes Eingabebeispiel
{
"n": 1,
"edges": [],
"claim": {
"edge_order": [],
"systems": [
{
"rotations": [
[]
],
"faces": [
[]
],
"genus": 0
}
],
"count": 1,
"genus_histogram": [
1,
0
]
}
}Ergebnis & Dokumentation
Maschinenlesbare Dokumentation dieses Hubs
Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.
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