Ещё одна кастомная версия модели Омега Керфуса игры Voices of the Void - K3RF. Создан по концепту человека, что сделал 2д-арт lap.sha (с Вконтакте). Модель полностью с квад-топологией (кроме лица) и имеет единый меш по основным частям. К сожалению, из-за странной кривизны скетчфаьа я не могу показать вам версию с туфлями и рабочими ногами

Another custom version of the Omega Kerfus model of the Voices of the Void game - K3RF. It was created according to the concept of a person who made 2d art lap.sha (from Vkontakte). The model is completely quad-topological (except face) and has a single mesh for the main parts. Unfortunately, due to the strange curvature of the sketchfab, I can't show you the version with heels and work legs.




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blend file with rig, shape keys face, heels and etc. - https://open3dlab.com/project/1b1f5fb4-33c0-4f53-9aaa-14e6f99ffabc/
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K3RF (Omega Kerfus) - Voices of the Void

Shape Formula
Fibonacci Spiral Enhanced
r = a·φⁿ, φ = 1.618...
Summary
Golden ratio Fibonacci spiral enhanced

Learn
Origin & History
The Fibonacci Spiral Enhanced is part of Dmension's library of 2,307 parametric equations. It belongs to a rich tradition of mathematical form discovery spanning ancient civilizations to modern computational mathematics.

Mathematical Function
Golden ratio Fibonacci spiral enhanced The shape is defined by parametric equations mapping 2D parameters to 3D coordinates, encoding geometric properties, symmetries, and topological characteristics.
     
📦Volume
796688.8941 m³
Total 3D space enclosed by the surface, computed via triple integration
 
 🎨 Surface Area
1.826e+6 m²
Total area of the outer surface, computed from mesh triangles

⚖️ Mass
7.967e+8 kg
Volume multiplied by material density (m = ρV)

Fibonacci Spyral Enhanced

Beyond manual sculpting: this is pure computational topology. 
This model is the direct, deterministic 3D output of the Polytopic Archetypal Projection Protocol (PAPP).
The Origin: The mathematical seed is the "Flower of Life", the fundamental matrix of sacred geometry based on overlapping circles with hexagonal symmetry. Its 2D ratios were extracted and fed into our "algebraic transducer".
The Pipeline: The algorithm processed these constants via Continued Fractions and Pythagorean reductions, mapping the data onto a Fibonacci lattice in a 4D hypersphere ($S^3$). 
Finally, the space was projected into 3D via a Hopf fibration ($S^3 \rightarrow S^2$).
The Result (V309): The mathematical coherence of the Flower of Life does not produce chaotic noise. 
It forces the system to naturally collapse into a dense, highly interconnected, and topologically closed ($\chi=2$) spatial lattice. 
An architecture of pure algebraic mechanics.
Procedurally generated via the PAPP Framework (Python/SciPy/NetworkX).

Flower of Life V309 | PAPP Generative Topology

This is a computational visualization of the Hopf fibration, built from the exact map of S³ → S² and exported as a topological GLB scene.

Rather than approximating the structure with ad hoc torus geometry, the model is generated from true Hopf fibers and organized around the Clifford torus as the central reference shell. 

Visual hierarchy is deliberately reduced to a small set of visible elements: 9 hero fibers, 12 secondary fibers, and 12 atmospheric halo fibers, while the remaining fibers are suppressed to preserve clarity and silhouette. 

Phase drives cyclic color along the hero fibers, latitude shifts the shell climate from cooler to warmer regions, the Clifford torus is treated as an opaline luminous core rather than a simple shell. 

Mathematical checks remain precise, with Hopf base error at machine scale and the Clifford shell centered at base z = 0. Generated as a structured topological artifact balancing geometric fidelity, readability, and computational aesthetics.

Generated by PAPP Framework.

Hopf Fibration  — Cosmological Topology

Living Earth V3 is a full closed Earth mesh built from real external datasets, not just a textured globe. 

It combines WGS84 geodetic shape, ETOPO 2022 topography and bathymetry, Blue Marble surface color, the real EGM2008 geoid, and PB2002 tectonic boundary data in a single manifold object. 

The model also integrates gravity-aware logic through Somigliana normal gravity with free-air correction, plus a light PAPP informational encoding layered on top of the physical data. 

What makes it different from most computational Earth representations is that it does not isolate one layer only—texture, terrain, or tectonics—but preserves geometry, relief, geoid structure, and tectonic semantics together inside one exportable globe. 

It is not just a visual Earth model, but a topologically clean and semantically enriched planetary artifact.

Computationally built and generated in seconds as a unified manifold planetary mesh from real geophysical data by PAPP Framework.

Living Earth V3 | PAPP Framework

Beyond standard 3D modeling: a mathematical autopsy of an algorithmic prototype. This is the V4 projection of the 2D Islamic "Shamseh" seed, processed via the Polytopic Archetypal Projection Protocol (PAPP).

The Anatomy: 24 concentric perfect spheres (R²=1.000000 each), built by a single connected graph. Every vertex is placed by rotating exactly 137.508° — the golden angle (2π/φ²) — from the previous one. The same rule sunflowers use to pack seeds, projected onto 3D spherical shells.
Fibonacci Signature: Azimuthal FFT reveals spiral counts of N=8,13,21,34,55 — five consecutive Fibonacci numbers. Ratios converge to φ. This is not an Islamic rosette; it's a spherical sunflower.

Network: 110,480 vertices, 747,904 edges. 73.8% intra-shell, 26.2% inter-shell (adjacent only). Connectivity peaks at the penultimate shell (96% from center) and drops at boundaries — a topological edge effect.

A phyllotactic crystal in 24 layers. Raw generative topology.

Generated via PAPP Framework.

Shamseh V4 Spherical Phyllotaxis (110k) | PAPP

Beyond manual 3D modeling: this is a raw mathematical discovery. 
This structure is a reconstructed topological element extracted from the infinite catalog of the Polytopic Archetypal Projection Protocol (PAPP).
The Pipeline: Operating in Discovery Mode, the algorithm processes a 4D integer seed through Continued Fractions and Pythagorean reductions. 
It constructs a quantized Fibonacci lattice on a 4D hypersphere ($S^3$), then projects the coordinates into our 3D observable space ($S^2$) via a rigorous Hopf fibration.
Structural Data:A Convex Hull algorithm solidifies the raw point cloud into this hyper-dense topological crystal.Vertices: 1,336 Lines (Edges): 64,147 Triangles (Faces): 125,622 With over 64k interconnecting lines for just 1,336 vertices, this object represents a highly saturated, maximally connected spatial phase. 
It is not art; it is materialized algebraic mechanics.
Procedurally generated via PAPP Framework (Python/SciPy).

Element V1419: 4D Polychoron | PAPP

A (21,13) torus knot — where 21 and 13 are consecutive Fibonacci numbers F(8) and F(7). 

The ratio p/q = 1.61538... approximates the golden ratio φ with Δ = 0.0026, making this a topological embedding of φ convergence.

Anatomy: 218,400 vertices, 420,000 faces, 638,400 edges. Built with exact Frenet-Serret frames (TNB orthogonality verified to 0.000000). 

The tube is a true polygon mesh, not wireframe — 8,400 core curve points × 24-sided cross-sections.

Color = Geometry: Vertex color encodes local curvature κ (warm = high bending) and torsion τ (violet shift at twist peaks). 

Brightness tracks radial position on the torus. 48,000 unique colors, zero cosmetic.

Inner Ribbon: A Seifert-inspired ribbon surface (16,800 faces) runs inside the tube, revealing the knot's twist structure and linking number = 273.

Topology: 21 full azimuthal turns, 26 meridional crossings. Single connected solid.

Generated via PAPP Framework.

Fibonacci (21,13) Hyper Knot V2 (218k) | PAPP

Technically, this object is a one-stroke knot path materialized as a closed tubular mesh through the PAPP-OSG pipeline: discrete path construction, topologically verified, tube extrusion, and over/under weaving.
Generated, not hand-modeled: the Triquetra starts as a gate-constrained one-stroke path on a 28-grid trefoil domain, then becomes a Catmull–Rom ribbon and a 10-sided tube via parallel-transport framing and z-lift weaving. 
Result: 430+ controlled crossings in one watertight band.
It uses a trefoil / three-lobe Celtic domain arranged around 120° rotational balance, so the whole form reads as one continuous interlaced band rather than a flat emblem. 
In 3D, the classic triquetra becomes a compact woven sculpture with repeated crossings, rounded tubular volume, and a strong circular silhouette that preserves the symbolic threefold structure while giving it depth, weight, and architectural presence.

Generated by PAPP Framework.

Triquetra OSG |  PAPP

Beyond standard data visualization: this is a crystallized financial market.
This model is the exact 3D topological footprint of the Bitcoin market in Sept 2017, generated via the Polytopic Archetypal Projection Protocol (PAPP).
The Origin (Oracle Mode): Real market data (Close/Open, High/Low, Volume) from that highly volatile month was extracted and converted into a 4-dimensional integer seed.
The algorithm doesn't simply "draw" a chart. It uses these financial signals to drive an algebraic cascade, mapping the data onto a Fibonacci lattice in a 4D hypersphere ($S^3$).
The space is then collapsed into 3D via a Hopf fibration ($S^3 \rightarrow S^2$), mathematically guaranteeing a closed spherical topology ($\chi=2$).
The Result: The turbulence and price crashes of that infamous Sept have been transmuted into pure geometric density.
Financial fluctuations forced the algorithm to create structural hotspots of topological hyper-connectivity.
This is the unique spatial signature of that historical timeframe.

BTC Sep 2017: Financial Crystal | PAPP Oracle

**Kummer Surface K3 Flux** is a computational 3D visualization inspired by the Kummer surface, a classical K3 example obtained by resolving the quotient (T⁴/(±1)). 
In mathematics, the Kummer construction is known for its singular quotient structure and its 16 exceptional curves introduced through resolution. 
This object translates that logic into a PAPP flux geometry: a woven network of volumetric strands that suggests concentration, branching, and reconstructed continuity. 
Rather than serving as a literal algebraic model, the piece acts as a geometric interpretation of the Kummer idea—where singularity, symmetry, and smooth resolution meet inside a single topological-looking 3D artifact. 
It sits between mathematical visualization, abstract structure, and computational sculpture. 

Generated by PAPP Framework.

Kummer Surface K3 Flux | PAPP

This model is a deterministic TPMS-based porous filter generated with the PAPP protocol from a Schwarz P field and a balanced radial grading strategy. Compared with denser TPMS families, Schwarz P produces fewer, larger, and more direct flow channels, giving the structure a clearer cellular logic while preserving full topological closure.
The final validated mesh is watertight and manifold, with 0 boundary edges, 0 non-manifold edges, and 0 degenerate faces. 
Topology audit: genus 268.
Balanced version metrics: body porosity 0.5984, porous-region porosity 0.6701, surface area 33.2451, 1,565,940 vertices, 3,132,948 faces.
This piece is both a mathematical surface realization and an engineering-ready porous architecture, intended for studies of flow, filtration, topology, and fabrication-aware design.

PAPP TPMS Filter — Schwarz P

**Torus Fiber Elliptic CY Flux** is a 3D computational visualization of an elliptically fibered Calabi–Yau structure, where a torus (T²) is fibered over a lower-dimensional base. 
Elliptic fibrations are central in F-theory and in many geometric compactification models, where singular or degenerate fibers encode physical information such as gauge symmetries. 
This object reinterprets that architecture through the PAPP flux language: bundled volumetric strands, projected topological flow, and readable 3D connectivity. 
Instead of presenting the manifold as a conventional static mesh, the form emphasizes fibering, resonance, and structure-through-connection. The result is a geometric sculpture that points toward the logic of elliptic Calabi–Yau spaces while remaining a computationally generated artifact in its own right. 

Generated by PAPP Framework.

Torus Fiber Elliptic CY Flux | PAPP

Chakra 09 (Samanā) is a high-relief geometric disc from the PAPP Chakra Series (V2.1). 

The object's architecture is based on the Enneagram—a complex geometry of three interlocking triangles forming a 9-pointed star. 

Using the Polytopic Archetypal Projection Protocol, the 2D yantra is projected into a 3D manifold through phi-harmonic convergence (kappa = phi^{-4}). 

The surface features 14-step terraced ridges generated via line-distance Gaussian fields, creating a tactile "topological landscape" of meditation.

Technical Specs:Geometry: Enneagram / Nonagram (3x3 triangular symmetry).
Pipeline: 6-Stage PAPP (φ-RG → Continued Fraction → Pythagorean Triple → S³ Fibonacci → Hopf → Stereographic).
Topology: Validated 2-manifold, X=2 (Euler Characteristic), watertight mesh.
Complexity: ~57,170 vertices | 114,336 faces.
Symbolism: Integration of Gurdjieff’s "Fourth Way" dynamics with Vedantic cosmology.
A deterministic fusion of sacred symbolic grammars and algorithmic topology.

Generated by PAPP Framework.

Chakra_09_Samana_V2 | PAPP

This object is a computational reconstruction of Boy’s Surface, the classical immersion of the real projective plane (RP²) into 3D space. 

It is generated from the Bryant–Kusner parametrization on a projective disc with antipodal boundary identification, making the topology explicit rather than treating the surface as a simple smooth shell. 

The mesh contains 41,472 vertices and over 371k total edges, including ring, spoke, braid, triad, and seam families that reveal the internal organization of the surface and emphasize its characteristic threefold symmetry. 

Spectral encoding maps intrinsic geometric fields into vertex color and scale, turning the object into both a topological visualization and an informational geometric artifact. 

Because RP² cannot embed in 3D without self-intersection, the surface is shown here as an immersed form, where those intersections arise naturally from the topology itself.

Generated by PAPP Framework.

Boy Surface — Spectral Immersed | PAPP

LOKA 06 (Tapa) is a 360° spherical manifold exploring the "frozen music" of sacred architecture. 

This object maps the acoustic resonance residuals of the 56 Musical Pillars of the Vitthala Temple (Hampi) onto a high-resolution sphere via the PAPP pipeline.

Representing Tapo-loka (the plane of austerity and meditation), the geometry is generated by translating harmonic JI intervals into topological peaks. 

The relief follows a dual Lambert projection, creating a seamless 2-manifold that bridges 4D vibrational theory with 3D form.

Technical Specs:Series: LOKA V3 (Full Sphere)
Protocol: PAPP (4D-to-S3-to-Hopf projection)
Plane: Tapo-loka (Emerald, Gold, and Violet palette)
Mesh: 57,122 vertices | X=2 (Euler Characteristic)
Invariants: phi-harmonic scaling applied to acoustic frequency mapping.

A study in the convergence of lithic percussion, ancient resonance, and deterministic geometry.

Generated by PAPP Frameowork.

Loka Tapa - MusicalPillarsV3 | PAPP

Minor Chord Flux Tube converts a minor harmonic ratio into a braided geometric field. 

Built as a twisted bundle of continuous strands, it preserves the same structural logic as the major version but shifts the visual character toward something darker, denser, and more introspective. 

The object suggests musical melancholy translated into spatial form: a cable of harmonic tension, looping through itself with coherence and flow.

 Rather than representing sound as a waveform, it treats harmony as an organized topological path — a musical relationship made visible as a sculptural flux structure.

Generated by PAPP Framework.

Minor Chord Flux Tube | PAPP

High-fidelity analytical torus generated via the PAPP v3.1.0 system (Phase 7.5). 

This model represents the positive branch (f⁺) of a "Bonnet Pair"—a rare configuration in differential geometry where two non-congruent surfaces share identical metrics (isometry) and mean curvature.

Based on the 2025 research by Bobenko, Hoffmann, and Sageman-Furnas, this surface is a compact torus in ℝ³ with numerically verified isometry against its twin branch (f⁻) at machine precision (E_rel ≈ 10⁻¹⁴).


Technical Specifications:

• Topology: Closed Manifold Torus (Euler Characteristic χ = 0).

• Resolution: 80x80 (6,400 vertices, 12,800 triangular faces).

• Parameters: Optimized at the critical closure value τ* = 0.16006 (Ratio 1/1).

• Analysis: Validated via Spectral Gap and Persistent Homology (TDA).


Ideal for mathematical visualization, topological research, and computational geometry studies.

Generated by PAPP Framework.

PAPP Bonnet Torus f⁺ | Ratio 1/1 (Unison)

This model of Flower of Life features a sophisticated "rainbow mosaic" field where colors are indexed by a dual-center blending logic (nearest and second-nearest circle centers).

Technical Specs:Geometry: 19 interlocking circles with a unique 64-spoke central polar architecture and 256 angular divisions.
Relief: A 22-step vertical extrusion creates a tactile, terraced topography with recessed "dark grout" seams.
Topology: Validated 2-manifold watertight mesh with an Euler characteristic X="(genus-0).
Complexity: 61,058 vertices and 122,112 faces.
Visual Character:The design blends sacred symbolic grammars with a vibrant spectral palette and radial "sparkle" highlights. 
It transforms a classical 2D yantra into a complex 3D topological landscape, optimized for both digital rendering and physical materialization.

Generated by PAPP Framework.

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