pentagram
Enable an AI agent to recognise a pentagram, assess its geometric and representational state, and choose transformations or interpretations supported by evidence.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
Researched by: Codex + Grok
Purpose and description
Enable an AI agent to recognise a pentagram, assess its geometric and representational state, and choose transformations or interpretations supported by evidence.
A pentagram is the regular five-pointed star polygon with Schläfli symbol {5/2}, formed by joining every second vertex of five equally spaced points on a circle (equivalently, by the diagonals of a regular pentagon), whose intersections reproduce a smaller pentagon and whose length ratios are the golden ratio; the same five-pointed device is used as a religious, apotropaic, and civic emblem.
It can be Trace and classify a candidate using its vertices and crossing cycle.; Measure regularity and orientation against explicit tolerances and reference axes.; Construct or redraw a pentagram while preserving its connection pattern.; Propose completion of missing strokes with inferred portions identified.; Rotate, resize or restyle a depiction subject to its geometric and contextual constraints.; Attach evidenced interpretations without inferring the identity or beliefs of its bearer..
Distinguishing features
Trace whether five outer vertices connect in one closed cycle through nonadjacent vertices; an ordinary pentagon connects adjacent vertices without the star's crossings.
For a complete simple depiction, check for five inward crossings and a central pentagonal region; a filled five-pointed silhouette alone does not establish this internal construction.
Distinguish five long crossing segments from the ten alternating boundary segments of a five-pointed star outline.
Treat a surrounding circle as an associated component rather than a requirement for pentagram identity; record the contextual use of the name 'pentacle' separately.
Check connectivity before counting visible tips when strokes are obscured, decorated or distorted.
Scope
+ The five-vertex crossing cycle that establishes pentagram identity
+ Regular and irregular geometry, orientation and deformation
+ Visible strokes, crossings, gaps and reconstruction uncertainty
+ Relations to enclosing circles, inscriptions and composite designs
+ Attributed meanings and constraints on altering a particular depiction
- The physical condition and ownership of an object bearing a pentagram
- General models of polygons, star polygons and geometric construction
- Religious traditions, organisations and belief systems
- Complete heraldic, decorative or ritual compositions containing the figure
- Legal rights governing reproduction of the surrounding artwork or emblem
Characteristics
- Identity assessment
- confirmed crossing figure | probable depiction | ambiguous star | not a pentagram Separates observed construction from recognition based only on resemblance or a supplied label.
- Observed outer vertices
- count, with obscured or inferred vertices identified separately Tests the five-point structure without treating missing visual evidence as absence.
- Connection pattern
- five-vertex crossing cycle | partial cycle | silhouette only | incompatible | unresolved Provides a stronger identity test than the number of visible points.
- Geometric regularity
- regular within stated tolerance | irregular | perspective-distorted | unresolved Prevents ideal geometric properties from being assumed for every depiction.
- Orientation
- degrees for a selected tip relative to a named reference axis Makes rotation reproducible and avoids orientation labels without a frame of reference.
- Stroke completeness
- complete | intentionally interrupted | occluded | damaged | unresolved Determines whether tracing or repair requires inference.
- Enclosure relationship
- no enclosure | inside circle | touching circle | crossing circle | other enclosure | unresolved Separates the star figure from a composite symbol and records their spatial relationship.
- Interpretation attribution
- claimed meaning linked to an identified interpreter, context and supporting evidence Prevents a geometric form or orientation from being assigned a universal meaning.
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 5 bundles · 9 layers · 16 findings · 24 questions.
Star identity Establish whether the observed figure has pentagram construction.
Five visible tips alone do not distinguish a pentagram from neighbouring star forms.
Outer vertices
Identify the five outer vertices independently of decorative additions.
Five-tip evidence
Record which candidate tips belong to the star and which are missing, inferred or decorative.
- Which five outer vertices define the candidate figure? definition
- Are additional or missing tips explained by decoration, occlusion or a different star construction? boundary
Crossing cycle
Assess the connections that distinguish the figure from a pentagon or star silhouette.
Traceable star path
Record the closed five-segment route through nonadjacent outer vertices and the evidence for its crossings.
- Can the five outer vertices be traversed in one closed crossing cycle? definition
- Are the internal crossings visible, inferred from interrupted strokes, or absent from the depiction? boundary
Pentagram geometry Describe the figure's shape and placement without assuming ideal regularity.
Recognition, comparison and reconstruction depend on separating structural identity from geometric precision.
Regularity and deformation
Assess deviations from a regular pentagram and their possible causes.
Regularity assessment
Record geometric measurements, tolerances and uncertainty about distortion.
- How closely do the outer vertices fit equal angular spacing on a common circle under the chosen tolerance? measurement
- Does available evidence distinguish intentional irregularity from perspective distortion or drawing error? provenance
Orientation and frame
Locate the star relative to an explicit viewing or application frame.
Referenced tip direction
Record a selected tip's direction and any evidence that its orientation matters.
- What angle does the selected tip make with the named reference axis? measurement
- Which rotations preserve the intended use of this particular depiction? action
Stroke realisation Assess how the crossing figure is rendered and where its path is uncertain.
Gaps, overpasses and missing strokes can change what is observable without necessarily changing the intended figure.
Crossing treatment
Describe the visual handling of intersecting segments.
Intersection reading
Distinguish plain intersections from over-under treatments and accidental visual merging.
- At each expected crossing, are both segments continuous, is one interrupted, or is the junction unreadable? measurement
- Does crossing treatment encode an intended interlacing pattern or merely reflect the rendering method? provenance
Missing path evidence
Separate observed strokes from proposed completion.
Reconstruction limits
Record missing segments and the limits of justified restoration.
- Which portions of the five-segment cycle are directly observable and which require inference? boundary
- What evidence would justify completing each missing portion while preserving uncertainty? action
Symbol context and use Relate the geometric figure to its surrounding composition and evidenced interpretation.
An agent must distinguish geometric recognition from contextual naming, meaning and permission to alter the depiction.
Composite boundaries
Identify which elements belong to the pentagram and which belong to a larger symbol.
Enclosure and additions
Record circles, letters and other additions as related components with explicit boundaries.
- Which strokes form the pentagram itself, and which form an enclosure, inscription or surrounding emblem? boundary
- What source establishes the name used for this composite, including any use of 'pentacle'? provenance
Attributed meaning and editing
Connect interpretations and permitted transformations to evidence about this depiction.
Context-bound interpretation
Record who attributes a meaning and how that attribution constrains proposed edits.
- Who assigns a meaning to this pentagram, in what context, and on what evidence? provenance
- Would rotating the star, removing its circle or changing its crossing treatment alter its documented meaning or intended use? action
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Kinds and varieties
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Regular geometric pentagram {5/2} (the unicursal star polygon of density 2)
- Upright (one point up) pentagram as a Wiccan, neopagan, or ceremonial-magic emblem of the five elements
- Inverted (two points up) pentagram, including the Church of Satan Sigil of Baphomet
- Pentacle: a pentagram enclosed in a circumscribed circle (modern occult usage; historically the words overlap)
- Interlaced (over-under woven) pentagram versus a simple outline or a solid five-pointed star
- Vexillological Seal of Solomon pentagram (notably the green star on the flag of Morocco)
- Pythagorean or Hygieia pentagram used as a recognition emblem
- Spherical pentagram (Napier's pentagramma mirificum in spherical trigonometry)
- Which of these kinds and varieties hold for the sense of pentagram this model covers, and on what evidence? provenance
Identifiers and schemes
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Wikidata - Q18532 - Item commonly used for the pentagram; confirm against the live item before treating as a persistent key.
- Schläfli symbol - {5/2} - Regular star pentagon; {5/3} is the same figure traversed the other way.
- Unicode - U+26E4 - Named PENTAGRAM; siblings U+26E5, U+26E6, U+26E7 for interlaced and inverted forms. The solid five-pointed star is a different character (e.g. U+2605).
- Which of these identifiers and schemes hold for the sense of pentagram this model covers, and on what evidence? provenance
Standards and regulation
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- The Unicode Standard (Unicode Consortium) - character names and code points U+26E4-U+26E7 for digital pentagram glyphs.
- ISO/IEC 10646 (ISO/IEC JTC 1/SC 2) - Universal Coded Character Set, same pentagram repertoire as Unicode.
- National flag specification of the Kingdom of Morocco - a green five-pointed Seal of Solomon pentagram on a red field (do not cite a dahir number without checking the current text).
- Which of these standards and regulation hold for the sense of pentagram this model covers, and on what evidence? provenance
Real-world use
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Drawn in geometry and design as a golden-ratio construction (diagonals of a regular pentagon).
- Worn as jewelry and used on altars in Wicca and related neopagan practice, usually point-up and often as a pentacle.
- Used inverted, with a goat's head, as the Sigil of Baphomet by the Church of Satan.
- Displayed as the green interlaced pentagram on the national flag of Morocco; a pentagram also appears in Ethiopian federal flag design.
- Marked historically on doors and thresholds in German-speaking Europe as a Drudenfuß against spirits.
- Drawn as the gobōsei (五芒星) associated with Abe no Seimei in Japanese Onmyōdō.
- Encountered far more often as a solid five-pointed star on flags, rank insignia, and wayfinding, a neighbouring figure often loosely called a pentagram.
- Which of these real-world use hold for the sense of pentagram this model covers, and on what evidence? provenance
Typical measurements
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- number of tips (vertices) - 5 (exactly, for a pentagram) - count
- density (winding number) of {5/2} - 2 - dimensionless
- interior angle at each tip of a regular pentagram - 36 - degree
- central angle between adjacent tips - 72 - degree
- diagonal-to-side ratio of the generating regular pentagon (golden ratio) - 1.6180339887… - dimensionless
- typical pendant or amulet diameter - 10-50 - mm
- Which of these typical measurements hold for the sense of pentagram this model covers, and on what evidence? provenance
Failure modes and hazards
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- An inverted or even upright pentagram is read in many Christian and popular contexts as a Satanic mark, prompting social conflict, workplace or school bans, and vandalism of the symbol or of people who wear it.
- Irregular drawing that breaks five-fold symmetry and loses the inner pentagon and golden-ratio intersections.
- Cataloguing and icon errors that treat a solid five-pointed star, a pentagon, or a hexagram as a pentagram.
- Historical moral panics (including late-20th-century Satanic Panic) treating possession or display of the figure as evidence of crime.
- In the Faust/Drudenfuß tradition, a pentagram drawn with a gap is narrated as failing as a barrier - a literary hazard, not a physical one.
- Which of these failure modes and hazards hold for the sense of pentagram this model covers, and on what evidence? provenance
Regional variation
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- English-language occult practice often contrasts pentagram (star) with pentacle (star in a circle); historical sources use the words more loosely.
- German: Drudenfuß or Pentagramm, especially as a house-protection mark.
- Japanese: gobōsei / Seiman linked to Onmyōdō and Abe no Seimei, not to European Satanism.
- Maghreb and parts of the Islamic world: five-pointed Seal of Solomon (khatam Sulaymān) as a protective and civic emblem, as on Morocco's flag.
- United States and much of Christian Europe: point-down pentagram widely coded as Satanic; Wiccan communities treat point-up as the default benign form.
- Many national flags use a solid five-pointed star with no occult meaning; calling those pentagrams is common in speech and misleading in a registry.
- Which of these regional variation hold for the sense of pentagram this model covers, and on what evidence? provenance
Neighbouring kinds and how to tell them apart
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- regular pentagon {5} - A pentagon is convex; its sides meet only at the five vertices. A pentagram is a star polygon whose sides cross, forming an inner pentagon.
- hexagram / Star of David - Count the tips: six versus five. A hexagram is typically {6/2} as a compound of two triangles, not a unicursal {5/2}.
- pentacle - In modern occult usage, look for a circumscribed circle around the star; historically the two names were often synonyms, so the circle test is conventional, not ancient.
- solid five-pointed star (heraldic mullet; Unicode BLACK STAR) - A filled silhouette has no inner pentagon. The linear pentagram shows crossing strokes and a small pentagon in the centre.
- heraldic cinquefoil - A cinquefoil has five curved lobes like a flower, not five sharp star points.
- Napier's pentagramma mirificum - A spherical figure of five right-angled arcs on a sphere, used in spherical trigonometry, not the planar star polygon {5/2}.
- heptagram {7/2} or {7/3} - Seven tips versus five; the construction uses every second or third vertex of a heptagon, not a pentagon.
- Which of these neighbouring kinds and how to tell them apart hold for the sense of pentagram this model covers, and on what evidence? provenance
Sources
- Pentagram - Wikipedia, Wikimedia Foundation - Geometric definition {5/2}, golden-ratio intersections, cultural uses (Pythagorean, occult, Drudenfuß, Moroccan flag), and distinction from pentacle and solid five-pointed star.
- The Unicode Standard, Miscellaneous Symbols (U+2600-U+26FF) - Unicode Consortium - Encoded character identities U+26E4 PENTAGRAM, U+26E5 right-handed interlaced pentagram, U+26E6 left-handed interlaced pentagram, U+26E7 inverted pentagram.
- Regular Polytopes, 3rd ed. - H. S. M. Coxeter, Dover Publications - Star polygons, Schläfli symbol {5/2}, density 2, and the identity of {5/3} with the opposite traversal of the same pentagram.
- Harmonices Mundi (1619) - Johannes Kepler - Early systematic treatment of regular star polygons, including the pentagram, as geometric figures rather than only as emblems.
What the second pass must settle
- Does the registry intend 'pentagram' to cover the geometric figure, symbolic depictions, or both, given the missing definition?
- Should filled five-pointed silhouettes qualify through documented intent, or remain related star depictions without visible pentagram construction?
- What minimum evidence and geometric tolerances should distinguish a distorted or incomplete pentagram from an ambiguous star?
- Which contextual naming conventions govern the relationship between 'pentagram' and 'pentacle' in the catalogue?
- Which authoritative sources should support interpretation and alteration constraints for particular cultural or historical uses?