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  • Platonic Structures - What are they?

    3D complex structures assembled using only two types of elements - nodes and struts. Any imaginable shape can be assembled in this way.

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  • How do I make one?

    Ever wonder how to put together real complex structures - as the one seen here? Don't worry; we are here to assist you along the way.

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  • Step 1. Choose your structure

    Select the structure you want to build from a large selection available on this site. Explore it using the 3D interactive environment.

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  • Step 2. Build Nodes

    Every node is build from 12 identical interlocking rhombic shapes. When oriented accordingly, faces lock to each other to form a closed shape.

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  • Step 3. Struts

    Joint nodes are connected to other joint nodes using only one type of connector.

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  • Step 4. Start Building

    Start connecting the nodes with struts and watch your structure grow.

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  • We Are Your Guide

    We will guide you every step of the way. A variety of clues, maps and 3D views are always just a click away.

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  • A GPS-Like Tool

    You can locate any node in the structure using our patented method - you are never lost.

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US Patent...

Stereographic Projections...

About Us

Mission statement: To change minds, to open eyes, to educate and inspire people designing and building better worlds.

Beauty makes beautiful things beautiful!

A sphere can be completely surrounded by exactly twelve other identical spheres. Close-packing of spheres helps us explore the shape of the physical space. A good design of a 3D structure shall obey the principles, freedom, and constraints imposed by the physical space around us.

Platonic Structures are complex 3D structures assembled from simple components using the patterns imposed by the close-packing of spheres.
We have developed and patented ( in US and Canada ) software tools and methods for designing Platonic Structures and for guiding an operator to assemble these structures.
Research is currently underway for using image processing and automation in assembling Platonic Structures.

If you are mathematically inclined and want to learn more about the CPS Geometry - the Geometry of Close-Packing of Spheres, or the Geometry of Close-Packing of Singularities - read my recently published book, available below.
We value your opinions and suggestions - Please provide feedback.

Book - CPS Geometry...

© 2016-2022 Platonic Structures Inc. All right reserved.

  • Imagination

  • Originality

  • Creativity

  • Utility

  • Vision

All Videos - List...

CPS Geometry Viewer...

PDF Files...

Written by the same author, the following book is an investigation into the nature of prime numbers and their role in understanding the physical Universe. The world is never the same for someone who has been to the summit and has contemplated the surroundings from that advantage point. There is no way back for the mind, there has never been a way back.

Book - Complex Arithmetics...

Author...

Main Ideas

Sometimes when few seemingly unrelated ideas come together they can create amazing things. Take for example these ideas:
© 2016-2022 Platonic Structures Inc. All right reserved.

Close-packing Equiradius Spheres

Close-packing

A sphere can be completely surrounded by exactly twelve other identical spheres. An amazing number of patterns and structures can be formed and be discovered in these arrangements. Feel free to explore.

Building Structures from Simple Elements

Structures

Use the patterns discovered and imposed by the close-packing of spheres to build complex 3D structures. Only two types of elements are needed: nodes able to be connected to up to 12 neighbors, and struts.

Determining the Location of a Node

Localization

The colors of the faces connecting a node to its neighbors provide the location of the node in the 3D structure. When assambling Platonic Structures, this GPS-Like Tool can help you any step of the way.

Physical Implementation

3D Structures are built from identical nodes ( universal connectors ) connected with each other using identical struts (links).Two patterns are available for you to use: square or hexagonal.
© 2016-2022 Platonic Structures Inc. All right reserved.

The Platonic Structures Box and its Content

The PS Box

Explore the content of the Platonic Structure Box by playing with this 3D animation. Get familiar with the Platonic Bricks (red, yellow and blue), the Struts and the Platonic Tools (the PS Holder, the PS Shell and the PS Ruler).

Learn How to Build a Node from Rhombic Shapes

The PS Node

A typical node is assembled from 12 identical rhombic shapes. When arranged properly these 12 shapes come together to form a rhombic dodecahedron. Each face has a central hole – to connect it to its 12 neighbors.

Learn How to Assamble a Platonic Structure

12 Neighbors

After playing with this 3D animation you will know how to assamble a Platonic Structure. By understanding how a node can be connected to all its twelve neighbours, you are ready to assamble any other Platonic Structure.

3D Visualization

3D Structures are built from identical nodes ( universal connectors ) connected with each other using identical struts (links).Two patterns are available for you to use: square or hexagonal.
© 2016-2022 Platonic Structures Inc. All right reserved.

Learn Basic Components - Nodes and Struts

Explore

Few types of nodes are available. Each structure requires only one type of node. Every node can be connected with up to 12 neighboring nodes. The connection pattern is determined by the close-packing of spheres. The links are colored.

Typical Platonic Structure - Square Lattice

Explore

Multiple nodes can be connected in square patterns to form planes. Nodes from these planes can also connect with the nodes from the planes above and the planes below. These are square 3D Platonic Structures based on square lattices.

Typical Platonic Structure - Hexagonal Lattice

Explore

Nodes can also be connected in hexagonal patterns to form planes. Each node can connect with up to 6 nodes inside a plane. Nodes can also connect with the nodes from the plane above and the plane below. These are hexagonal 3D Platonic Structures.

Albums...

All Structures - List...

Platonic Structures

These Structures are built from identical nodes connected with each other using identical struts (links). Two patterns are available for you to use: square or hexagonal.
We are working hard to add more structures on this website for you to build. Check back soon for further updates.
© 2016-2022 Platonic Structures Inc. All right reserved.

Hints From Our Awesome Team

"There are three constants in life... change, choice and principles." Stephen Covey

A Compass

Know your orientation

When exploring, if you don't want to get lost, you need a compass. Building these structures requires only a basic awareness of the orientation. A coordinate system is always available to orient your structure on the screen. Always imagine a corresponding coordinate system in the physical world where the construction takes place.

The Seed

First Plane Comes First

Start with the first plane - the base plane. The map (nodes configuration) of the first plane is available for you to explore and consult at any time. Use both the image or the 3D format to help with the assembling. Don't forget the orientation of the first plane; it will dictate the orientation of the entire structure.

One Plane At A Time

What floor are you on?

Never work on two or more planes at the same time. Once you started assembling a plane - complete it before moving to the next plane. Again, use all the tools available to you to explore and consult where you are in the structure. Tool are available to isolate and display any plane in the structure and explore.

Use "Find Location" Tool

Where are you?

A GPS-like feature - the "Find Location" tool is always just a click away. Make good use of it! Switch between low level view to overall view to know where you are. There are also "Plane Views" and other tools available. From time to time, check and re-check the completed parts of your structure.

Best Prices Guaranteed

The Platonic Box and Sets of Platonic Bricks and Platonic Stratus are available here: platonic-structures.myshopify.com

Small Set

$ 25/kit

- choice of three colours -
144 Platonic Bricks
12 Platonic Nodes
60 Struts
Bricks colur: Red, Yellow or Blue

Buy...

Platonic Box

$ 60/box

- mixture of three colours -
432 Platonic Bricks
36 Platonic Nodes
200 Struts
Bricks colur: Red, Yellow and Blue

Buy...

Medium Set

$ 160 /kit

- choice of three colours -
3000 Platonic Bricks
250 Platonic Nodes
1000 Struts
Bricks colur: Red, Yellow or Blue

Buy...

Large Set

$ 300/kit

- mixture of three colours -
6000 Platonic Bricks
500 Platonic Nodes
2000 Struts
Bricks colur: Red, Yellow or Blue

Buy...

New Platonic Structures

Steps we take to add new Platonic Structures to this web site. Check back soon for further updates.

Design
Implementation
Web Availability

Other Applications

The principles and methods for designing and assembling Platonic Structures and for determining locations inside these 3D structures
can have a variety of applications. Few of these applications are presented below.
If you are interested and want to get involved (collaboration, partnerships, investment, etc.) please contact us.
© 2016-2022 Platonic Structures Inc. All right reserved.

  • Check back soon for further updates.

    - Smart Constructions In Space

  • Check back soon for further updates.

    - Nanotechnology

  • Check back soon for further updates.

    - 3D like Printing

Creativity Components

These are the elements that help you recognize creativity. Do you see them in Platonic Structures?

Surprise

"Most things in life come as a surprise."
Lykke Li

Originality

"Be Original. Copies fade too fast."

Beauty

"Beauty in things exists in the mind which contemplates them."
David Hume

Utility

"Nothing can have value without being an object of utility."
Karl Marx

Get in Touch

“If you have an apple and I have an apple and we exchange these apples then you and I will still each have one apple. But if you have an idea and I have an idea and we exchange these ideas, then each of us will have two ideas." George Bernard Shaw

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