Polyhedral Cathedral

marble_floor_mosaic_basilica_of_st_mark_venice-250x250The die cut paper sat in the attic at the farm for more than 20 years.
Sat in the dark. Forgotten.
But when found. and assembled.

          in precise angular fulfillment of the cosmic law
          of eternal return
          crags canted and sloped like dolomitic spikes
          edges of a dream
          denoting polyhedral passage
          from one destiny to another

The die cut paper
A covenanted ark
A cathedral for geometers.

This would be the stuff of mysteries
Of course
The fashioning of the die cut paper
Into lamps that
(20 years after the fact)
Illumine the secret key or the encoded message or the sections of the map
That disclose the hidden treasure, the fatal words, the smiting hand, the spinning gyre.

But 20 years too late, unfortunately, we can only remember what did happen, not what might have been.


Arpad is returning to Budapest
(60 years after the fact)
this decision/need to return
(perhaps only with difficulty as he weighs nearly 300 pounds)
Precondition for discovery of
The die cut paper sitting alone, in a stack, in the attic at the farm for more than 20 years

Arpad’s return,
A sad-kind homecoming, embracing
the physics of loss
the compression of time
the what happened in-between?

Giantic emotionally needy komondor
(we become our dogs)
Folding in upon himself
A polyhedron reduced to being no more than a
Stack of die cut paper.


In Hungary, in the 16th century, the Hungarian Reformed Church self-assembled
An exhalation
Floating and unwinding and rising from its Roman interrogators
Spinning away from Lutheran progenitors
The Synode of Debrecen.

Self-naming and self-identifying Protestants
Their sacred buildings house the spirit of self-referentiality – this is me.

And so
Protestant churches housed the individual
A new kind of human

And so
To fully separate
From Rome’s cross-hatched symbology.
Hungarian village churches adopted the star.

To beacon
From the pinnacle of the spire
Their blessings and their curses
As children of God.

In the 19th-century in Hungary
As a means of production
(the production of tower spires)
Enabled by new copper and zinc fabrication methods
Aspiring churches could select an adequate shape of star polyhedra
(as a three-dimensional object)
From zinc factory catalogues offering a wide variety of tower spires.

Primarily the rhombicuboctahedron
Although not without a sampling of
Dipyramids, rhombic pyramids, and truncated square pyramids
(the pyramids technically not polyhedra
just cheap knockoffs
geometric forms attached to a spheroid center
lower-priced items in the zinc catalogue).


Protestantism then
Even in Hungary
Village by village

Stacks of die-cut paper
Lifting and folding into each other
Solids emerging from surfaces
Faces meeting in pairs
Edges meeting at the vertex
resolution of all space into a single dimension
a dense unifying moment
The vertex a pivot.


Leonardo’s radiant polyhedral illustrations for Luca Pacioli’s The Divine Proportion (1509)
Included a stellated octahedron
Simplest of the five regular polyhedral compounds
A three-dimensional extension of the hexagram
Formed from two centrally symmetric overlapping tetrahedral polygons
With fractal potential.

But we owe it all to Kepler
Who represented the universe as a series of nested polyhedra on which the planets rotate.
Who named Leonardo’s stellation the stella octangula.
Who also stellated the regular convex dodecahedron
For the first time treating it as a surface (a gram), not a solid.

This is what Kepler noticed.
By extending the edges or faces of the convex dodecahedron until they met again,
He could obtain star pentagons
And from the regularity of these pentagons
Which Kepler also recognized
He constructed stellated dodecahedron
Which concealed the central convex region within the interior
With only triangular arms visible
Not a sphere!
Not a knockoff.
A geometrically regular polyhedron!


Leonardo anticipated C60
600 years ago
C60. Welcome to the Fullerene Family!
(In common parlance) the family of Bucky Balls
(and other Bucky things)!
C60. A polyhedron, of course. A truncated icosahedron (think soccer ball)
          with 60 vertices and 32 faces
20 hexagons and 12 pentagons where no pentagons share a vertex
with a carbon atom at the vertices of each polygon and
a bond along each polygon edge

Buckminsterfullerene is the most common naturally occurring fullerene molecule
With philosophically significant emergent properties
Indicated by unusual optical absorptions in thin films of carbon dust (soot)
(geometric perfection dirt-embedded)
With solid and gaseous forms of the molecule detected in deep space
One of the largest objects shown to exhibit wave-particle duality.
C60 dissolved in olive oil nearly doubled rodent life spans.
Possibly also useful for photovoltaic applications.


An OG of solar photovoltaic technology
Explored physical properties of light (photonics)
Its conversion to electricity
Via the photovoltaic semiconductor.
His specialty thin-film conduction
In which we take starlight
Heaven’s pinpricks
Stellated energy of infinite scope
Condensed via tetrahedrally bonded solar cells
Possessing exceptionally high light absorption coefficients

Thin-film solar cell companies include Nanosolar (bankrupt) and Solyndra (bankrupt).
Leaving alive only spiritually dead
First Solar, with thin-film technology dependent on Cadmium
Super-toxic heavy metal
Extracted from zinc
A new means of production, yes.


The polyhedral cathedral.

Antoni Gaudi’s Sagrada Familia.
His polyhedra in the church towers spawning a new class of hollow carbon-cage molecules.
Gaudi, in latter stages of his own design journey
Returned to more formal expression
I am a geometer, he said.
But he lived in the details.
Each architectural moment unique.

Philip Johnson’s Glass Cathedral
Sanctifies light
With its free-form polyhedral skin defying geometry
If not passivity
The tent meeting reborn
To serve the theatrical broadcast ministry
The Hour of Power
Of televangelist Robert Schuller (bankrupt).
A simulacrum of Great Awakenings
With a spillover parking lot where a drive-in congregation
Listens to the sermon from their car stereos.

Philip Johnson’s own oddly antiseptic (formerly fascist) conservative politics here
Oddly implicated
In the service of empty crystalline perfection.


The die cut paper sat in the attic at the farm for more than 20 years.
Sat in the dark. Forgotten.
But then found. and self-assembled.
Through some inner compulsion.
Obedience to hard-coded instructions?
Or to divine imperative?
No matter.
What matters is our urgent will to emerge from
(not into)
A light.

Each polyhedron glows, warmly, from within.
Alight. Pulsation of different hues and intensities.
We are singularities.
Cathedrals unto ourselves.
With facets and edges and vertices that allow us to connect and merge.
We join at the vertex (our dense unifying moment).
We pivot toward each other.
Without self-effacing.

Each of us illuminated
By a grace of our own making.


In Budapest.
Under the starlight.
Nuzzles his komondor.

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