Golden Intonation
$3.99
A FRACTAL PYRAMID BY SEVAN BOMAR
Tetra
Also known as the Tetrix — the Sierpiński tetrahedron rendered as an object of contemplation. Four pyramids within one, repeated without end, holding the shape of infinity in the space of a room.
Behold the Form
FORM · RECURSION · INFINITY
Take a tetrahedron. Halve it, and set four smaller copies at its four corners. Do it again. And again. What remains is Tetra — a form that grows more intricate at every scale, whose volume dissolves toward nothing while its surface never diminishes. A work of art in the shape of a question: how much can be held by almost nothing at all?
THE GEOMETRY
The shape that contains itself
Tetra is the three-dimensional kin of the Sierpiński triangle. Its rule is simple and its consequence is endless: every part is a smaller whole. Mathematicians call this self-similarity. The ancients would have called it a mirror.
Four Within One
Each tetrahedron is made of four half-scale copies of itself, one at each vertex, leaving an octahedral void at the heart.
Dimension Exactly Two
Its Hausdorff dimension is log 4 / log 2 = 2. A form living in three-dimensional space that is, in measure, pure surface.
Constant Surface
At every iteration the total surface area stays exactly the same — four copies at one-quarter the area each.
Vanishing Volume
Each step halves the volume. Carried to infinity, Tetra encloses nothing — and yet it is undeniably there.
The Iterations
The volume vanishes. The surface remains.
Every step multiplies the tetrahedra by four and halves their edge. Read the last column slowly.
LevelTetrahedraEdgeVolumeSurface
001111
0141/21/21
02161/41/41
03641/81/81
042561/161/161
051,0241/321/321
064,0961/641/641
Dimension · log 4 / log 2 = 2
Correspondences
What the form has meant, across the ages
Tetra makes no claims. It simply stands where these ideas have always stood.
PLATO · TIMAEUS
Fire
Plato assigned the tetrahedron to fire — the sharpest and lightest of the solids, the one that rises. Tetra is that flame, refined into flame within flame.
PYTHAGORAS
The Tetractys
One, two, three, four — ten points arranged as a triangle, the Pythagorean emblem of the cosmos unfolding from unity. Lifted into space, the tetractys becomes a tetrahedron.
FIRST SOLID
The Simplex
Four points are the fewest that can enclose space. The tetrahedron is the first room — the seed of every solid that follows.
NUMBER
Pascal’s Pyramid
Shade the odd entries of Pascal’s triangle and the Sierpiński triangle appears. Do the same to Pascal’s pyramid, and Tetra emerges from pure arithmetic.
PROJECTION
The Full Shadow
Seen from the right angle, this form of vanishing volume casts a solid, seamless square. Almost nothing, throwing a complete shadow.
ORIENTATION
Four Directions
Four faces, four vertices, six edges — a compass of the whole. Tetra sits in a room the way a cardinal point sits on a map.
Infinity, held in a form small enough to sit on a table.
THE CONTEMPLATION
How to sit with Tetra
01
Place
Set it where light moves across the day — a windowsill, a desk, an altar. Its openings catch shadow differently every hour.
02
Trace
Follow one edge with the eye into the next scale, and the next. Notice the moment the pattern outruns your attention.
03
Return
Come back to the whole. The largest form and the smallest are the same shape. Let that be enough.
Design
Sevan Bomar
Form
Sierpiński Tetrahedron
Dimension
log 4 / log 2 = 2
Size
10 × 10 × 7 in
Weight
3 lbs
Includes
Storage housing
QUESTIONS
Before you bring it home
Four within one, without end. Tetra is a small monument to the idea that the whole can be found in every part.
Tetra
$144.00
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