dodecadodecahedron
Enable an agent to recognise a dodecadodecahedron, validate its geometric representation, and choose operations that preserve or explicitly transform its identity.
Bundle → Layer → Finding → Questions Filled
6 bundles · 11 layers · 16 findings · 30 questions
Identity and recognition Establish whether a named or supplied object represents the registered dodecadodecahedron.
Name resolution
Resolve names and catalogue references without creating additional registry things.
Catalogue identity
Require catalogue names, numbering conventions, and geometric evidence to agree.
- Which source and numbering system identify the candidate as the dodecadodecahedron? provenance
- Does a qualified name denote this same object or a snub, truncated, or ditrigonal neighbour? boundary
Structural recognition
Apply the face and vertex tests that establish the intended polyhedron.
Alternating face test
Check the two face families and their alternating cyclic arrangement at every vertex.
- Does the candidate contain exactly 12 regular pentagons and 12 regular pentagrams? measurement
- Does every vertex have the cyclic configuration 5/2.5.5/2.5? definition
Incidence and crossings Preserve the mathematical connectivity through a self-intersecting realization.
Face boundary cycles
Record pentagons and pentagrams as ordered mathematical boundaries.
Pentagram traversal
Retain the star traversal instead of substituting a convex pentagon or a subdivided outline.
- Does each pentagram boundary follow the {5/2} traversal through its five vertices? definition
- Are rendering subdivisions mapped back to the original pentagram face and its five edges? boundary
True adjacency
Separate shared edges from geometric crossings.
Incidence integrity
Audit the declared connectivity independently of the displayed surface.
- Do the declared incidences recover 30 vertices, 60 edges, and 24 faces? measurement
- Which apparent intersections are absent from the mathematical incidence structure? boundary
- Does every mathematical edge connect its intended two faces without adding adjacency at crossings? definition
Metric realization Determine whether coordinates realize the uniform polyhedron at a declared scale.
Coordinates and scale
Make coordinate provenance, normalization, and precision explicit.
Normalized realization
Establish reproducible coordinates and quantify geometric error.
- Which construction or coordinate source generated the realization, and what edge length normalizes it? provenance
- What are the maximum normalized edge-length and face-planarity residuals? measurement
Uniformity validation
Check regularity and symmetry beyond equal edge lengths.
Regular faces and vertex orbits
Require both regular face geometry and a symmetry action relating all vertices.
- Are the pentagon and pentagram faces regular under their respective boundary traversals? measurement
- Do verified symmetries preserving the full face incidence act transitively on all 30 vertices? definition
- What numerical tolerance permits accepting this approximation for the intended operation? action
Surface interpretation Specify what filled faces, surface measurements, and displayed fragments mean.
Star-face interiors
Distinguish a pentagram boundary from a chosen filling of its plane.
Fill and orientation
Declare how the central region and overlapping regions of star faces are treated.
- Which fill rule determines whether the central pentagonal region of each pentagram is included? definition
- How are face orientations recorded for winding-sensitive calculations? measurement
Measurement and display
Keep mathematical quantities separate from visible fragments and mesh output.
Interpretable output
Attach the interpretation needed to reproduce rendered or computed results.
- Does a reported area measure filled face regions, count overlaps with multiplicity, or measure the visible exterior? measurement
- What interior or winding convention defines any reported volume? definition
- Can an export preserve the mapping from triangulated fragments to all 24 mathematical faces? action
Constructions and neighbours Track derivations and transformations without confusing related polyhedra with this entry.
Construction witness
Use a reproducible construction as evidence for the resulting incidence and geometry.
Rectification witness
Investigate the halfway truncation construction relating the great dodecahedron and small stellated dodecahedron. [Robert Webb's construction account](https://software3d.com/Dodecadodeca.php)
- Which starting polyhedron and truncation parameter reproduce the required alternating faces? provenance
- Does the constructed output pass the incidence and uniformity tests independently of its construction label? measurement
Identity-changing operations
Record the target and assumptions of operations that replace the original face structure.
Dual and derived targets
Treat the medial rhombic triacontahedron as a related dual, with a separate identity. [Robert Webb's dual identification](https://software3d.com/Dodecadodeca.php)
- Which duality convention and normalization are used to construct the medial rhombic triacontahedron? action
- After truncation, faceting, or mesh repair, does the result still satisfy this entry's defining incidence? boundary
- Which neighbouring registry entry should own a result that fails those identity tests? action
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Check these first
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these check these first hold for the sense of dodecadodecahedron this model covers, and on what evidence? provenance
Identifiers and schemes
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these identifiers and schemes hold for the sense of dodecadodecahedron this model covers, and on what evidence? provenance
Real-world use
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these real-world use hold for the sense of dodecadodecahedron this model covers, and on what evidence? provenance
Typical measurements
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these typical measurements hold for the sense of dodecadodecahedron this model covers, and on what evidence? provenance
Failure modes and hazards
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these failure modes and hazards hold for the sense of dodecadodecahedron this model covers, and on what evidence? provenance
Neighbouring kinds and how to tell them apart
Recalled without web access and unsourced; every item is a lead to verify.
- Which of these neighbouring kinds and how to tell them apart hold for the sense of dodecadodecahedron this model covers, and on what evidence? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
What it is Filled
The dodecadodecahedron is a nonconvex uniform polyhedron with 12 regular pentagonal faces and 12 regular pentagrammic faces, meeting alternately four at each of its 30 equivalent vertices.
In scope
- Recognition through pentagonal and pentagrammic faces and their incidence
- Distinction between mathematical edges and incidental geometric intersections
- Validation of regular faces, equal edges, and vertex transitivity
- Coordinate, face-cycle, and rendered representations of the same polyhedron
- Construction and transformation relationships that establish or change identity
Out of scope
- The general classification of all uniform polyhedra
- Independent models of the great dodecahedron and small stellated dodecahedron
- Independent models of snub, truncated, and ditrigonal dodecadodecahedra
- Material strength, fabrication tolerances, and manufacturing processes for physical replicas
- General mesh-processing algorithms unrelated to preserving this polyhedron's incidence
Why it exists Filled
Enable an agent to recognise a dodecadodecahedron, validate its geometric representation, and choose operations that preserve or explicitly transform its identity.
Distinguishing features Filled
- The face inventory is 12 regular pentagons and 12 regular pentagrams, with 30 vertices and 60 edges. [Robert Webb's model](https://software3d.com/Dodecadodeca.php)
- The cyclic face sequence at each vertex alternates pentagram, pentagon, pentagram, pentagon; face counts alone are insufficient for recognition. [Robert Webb's model](https://software3d.com/Dodecadodeca.php)
- Pentagram crossings and intersections between faces must not automatically become additional polyhedral vertices or edges. [Robert Webb's topological representation](https://software3d.com/Dodecadodeca.php)
- A candidate must satisfy uniformity through regular faces and symmetry-equivalent vertices; a star-shaped silhouette or a compound of dodecahedra does not establish identity.
What robots and AI may and may not do Filled
Must not
- Present an incorrect model or wrong face counts as accurate.
- Confuse it with similarly named star polyhedra in teaching material.
- Copy published images or models without credit.
Only with a human decision
- Publishing new claims about its properties under a person's name.
May
- Explain the dodecadodecahedron's faces, vertex figure and relation to other uniform polyhedra.
- Generate accurate models or images of it from verified coordinates.
Moral aspects Filled
- Accuracy and credit matter in mathematical teaching and publication.
Who is affected
- Students
- Mathematicians
- Model makers
Owners Filled
Steward
Nobody owns it; it is a concept of geometry.
Links to other meta-models Filled
parent
- Q2878957 - registry parent class
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.dodecadodecahedron
- Wikidata: Q3033696 (https://www.wikidata.org/wiki/Q3033696)
Direct properties not applicable Not applicable
- Face inventory: 12 pentagons {5} and 12 pentagrams {5/2}
- Incidence counts: 30 vertices; 60 edges; 24 faces
- Cyclic vertex configuration: 5/2.5.5/2.5, up to cyclic rotation and reversal
- Edge scale: Positive edge length a; dimensionless normalization or declared length unit
- Regularity residual: Maximum relative edge-length deviation and face-planarity residual divided by a
- Representation validity: Unverified; incidence-validated; geometry-validated; rejected
- Face-interior interpretation: Boundary-only; even-odd fill; winding-based fill; explicitly specified alternative
Plane XCT: no invented physical properties.
Recognition optional Filled
- Twelve pentagons and twelve pentagrams crossing through each other, four faces at each vertex.
Capabilities and actions required Filled
- Validate a candidate using face cycles, incidence counts, regularity, and symmetry
- Generate or compare coordinate realizations under rigid motion and uniform scaling
- Render pentagonal and pentagrammic face families separately to expose their incidence
- Compute geometric quantities after declaring normalization and intersection conventions
- Construct related polyhedra while recording when the result leaves this registry identity
- Export a visual or fabrication representation with mathematical faces mapped to output pieces
Hazards and failure modes required Filled
- Self-intersecting faces are easily mis-rendered by software.
Standards and interfaces not applicable Not applicable
Not applicable
No specific standard, law or official classification applies to this abstract polyhedron as such.
Context of use required Filled
- The dodecadodecahedron is encountered in the study of uniform polyhedra, symmetry and nonconvex geometry.
- Mathematical models and computer graphics use it to explore intersecting faces and the distinction between geometric surfaces and solid boundaries.
- Validating a representation requires preserving its pentagonal and pentagrammic faces and their incidence relationships.
Sources Filled
- Wikidata item Q3033696: dodecadodecahedron - identity and sense of the item
- Wikipedia: Dodecadodecahedron - general description of the item
Open questions
- Which exact coordinate construction should be the canonical validation reference, and what approximation tolerances suit different uses?
- How should catalogue identifiers be reconciled when an implementation's numbering differs from a published enumeration?
- Which face-filling and volume conventions should Vercy require for comparable measurements of this self-intersecting polyhedron?
- Which topological invariants should be recorded for the abstract incidence surface, and how should they be distinguished from invariants of a subdivided spatial image?
- Does the existing world-model catalogue already cover this concept, requiring this registry entry to link to that publication?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q3033696/spec.json