Try itInterfaceEffectsThe mathCapture
iPad · spatial art

Procreate for polyhedra.

Summon a mathematical solid, then bend it with light and motion. Try the controls — this is the real renderer.

Summon a solid
Spin
Explode
Shells
Hue
Group orbit
Real menus, real maths — colours use Athena's harmony formulas; Shells is the OBB cage stack.
V·E·F12 · 30 · 20
DualDodecahedron
Dihedral138.19°
FacesTriangle
the idea

A studio for solids, on a canvas of light.

Athena turns pure geometry into a living scene. Tap to summon, drag to arrange, and let effects run while you compose.

44 solids, one tap

From the five Platonic solids to Archimedean, Catalan, Kepler–Poinsot and Johnson — every shape derived from clean geometry.

Effects that move

Spin, colour harmonies, explode, glowing shells and 30+ particle trails — all live, all at once.

Capture in motion

Shoot a photo or record video straight from the scene, then save and share.

the interface

Every control, one thumb away.

A SwiftUI surface floats over the SceneKit scene: pick a tool from the strip, dial it in on the right dock, and group your solids with selectable chips.

  • Tool strip — Motion, Appearance, Explode, Shells, Trails, Layer and Group.
  • Settings dock — sliders for whatever tool is active, bound to every selected object.
  • Undo / redo — floating buttons that step through 50 snapshots without moving your camera.
  • Menus everywhere — spin axis, render quality and 14 colour harmonies, one tap each.
Pause
Untitled scene
G1 · 12
G2 · 6
Shells · OBB
Count · 3
Spacing
Glow
Breathe
Solids
× 12
HD ▾
the effects

Pick a tool. Watch it come alive.

Effects are stored per object and per group, so a single scene can hold dozens of solids each doing their own thing — and every value saves with the file.

Spin

Tumble, or lock to X · Y · Z, with a per-layer stagger.

Colour harmonies

14 wheel patterns — Rainbow, Golden, Triadic, Neon, Ice — recolour the whole set live.

Explode

Blow faces outward in up to six nested layers, with spacing and fade.

Shells · OBB

A stack of glowing cages that follow the shape — pulse, breathe, rotate, rainbow.

Particle trails

Over 30 types — comet, fire, plasma, lightning, chromatic — plus zoom-reactive warps.

Size variation

Five channels multiply: per-object, Fibonacci, Euler density, Kepler nesting, F/V duality.

Group spin

Orbit a whole cluster about its centroid; reverse it, or tilt freely with two fingers.

Travel path

Send a group along an XYZ route — "beads on a wire" — looping or one-shot.

Lighting & glow

Steer the key light by azimuth and elevation; push object luminance into bloom.

Render quality

SD · HD · Ultra — antialiasing and supersampling on tap.

Zoom-FX

Trails react to the camera — warp streaks, vortex and burst on zoom.

Save · load · undo

Whole-scene snapshots to .athena, reloaded exactly as they were.

the math

Four solids, typed by hand. The rest is derived.

Coordinate tables are where errors hide. So Athena hand-types only the tetrahedron, cube, octahedron and icosahedron — then grows the whole catalog with a handful of geometric operators.

The icosahedron's twelve vertices are just the cyclic permutations of one pair of numbers — built from the golden ratio:

// golden ratio
φ = (1 + √5) / 2 ≈ 1.6180

// 12 vertices, all permutations of
( 0, ±1, ±φ )  ( ±1, ±φ, 0 )  ( ±φ, 0, ±1 )

// then normalise every solid to
circumradius = 2

Operators always produce correct topology. The geometry comes out clean and consistent — exactly what an art tool needs, without a brittle table of hand-keyed coordinates for the whole catalog.

// dual swaps faces ↔ vertices
dodecahedron = dual( icosahedron )

// soccer ball = truncated icosahedron
result = truncate( icosahedron )
// 12 pentagons + 20 hexagons

The catalog — five families

Platonic 5

All faces the same regular polygon; every vertex identical.

Archimedean 11/13

Two or more regular polygons, every vertex identical. Two snubs still to come.

Catalan 11

The dual of an Archimedean — every face congruent, vertices vary.

Kepler–Poinsot 4

Regular star polyhedra with star-polygon faces or vertex figures.

Johnson 13

Convex, regular-faced, non-uniform — a procedural subset, built piece by piece.

Five operators do the work

d

Dual

Swap every face for a vertex. Turns an icosahedron into a dodecahedron.

a

Ambo

Rectify — cut to edge midpoints. The route to most Archimedeans.

t

Truncate

Slice off each corner, opening a new face where a vertex was.

k

Kis

Raise a pyramid on every face — the basis of the star forms.

c

Chamfer

Bevel every edge into a hexagon — the Goldberg-style geodesic operator.

How each family is born

Platonic truncate / ambo Archimedean dual Catalan
Platonic kis · stellate Kepler–Poinsot ·  and Johnson · composed by hand

The Johnson family is the exception to the operator chain — its pyramids, cupolas and bipyramids are composed procedurally, piece by piece (13 in the catalog so far, of 92 known).

Every result still obeys Euler's formula. For the truncated icosahedron: V − E + F = 60 − 90 + 32 = 2
from scene to story

Every moment is a shot.

Frame it, hit record, and walk away with a file ready to post. Athena keeps your work safe, frame by frame.

  • Photo & video — hi-res offscreen stills and smooth H.264 capture.
  • Scene gallery — save the whole scene to .athena and reload it exactly as it was.
  • Undo, always — step back through 50 snapshots without losing your view.
REC
SpinAurasTrailsLayer
the craft

No shortcuts. Apple frameworks only.

Built in SwiftUI over SceneKit with zero third-party dependencies — so it stays fast, native, and entirely yours.

44
solids in the catalog
64
per group, one tap
0
outside dependencies
iOS 16+
iPad-native

Make something
impossible.

Athena is coming to iPad. Bring the geometry — we'll bring the light.