I’ve been fascinated with the crazy interlocking shape models that Byriah Loper has been designing for years now.

You may have heard of the Five Interlocking Tetrahedra model before. It’s pretty popular, here’s a video showing its assembly.

I’ve tried a couple of times to put this together but I can never get the 5th one to fit in properly. If you want to try folding this model yourself you can follow the video or check out the original instructions here.

Byriah Loper’s models are on another whole level from this.

His models are already amazing but if you’re into math at all then you’ll probably enjoy these even more.

These are my top 20 favourite photos of his work. All models are designed and folded by Byriah Loper.

If you’re interested in learning more about the design and math behind these models click through to the original image on Flickr and check out the description.

 

Growing Rhombi
Image source: https://www.flickr.com/photos/byriahloper/21893273995/

“Growing Rhombi” (Level 5) Three Interlocking Octahedrically Distorted Octahedra

Instructions available from Byriah Loper’s Flickr

 

Five Interlocking Deconstructed Octahedra
Image source: https://www.flickr.com/photos/byriahloper/20884624110/

Five Interlocking Deconstructed Octahedra

Instructions available from Byriah Loper’s Flickr

 

Twelve Interlocking Decagonal Stars + Twelve Interlocking Pentakaidecagonal Stars (Byrah Loper)
Image source: https://www.flickr.com/photos/byriahloper/19882022370/

Twelve Interlocking Decagonal Stars + Twelve Interlocking Pentakaidecagonal Stars

Instructions not available

 

Origami Lanterns
Image source: https://www.flickr.com/photos/byriahloper/19509455830/

“Lanterns” Six Interlocking Irregular Monotruncated Octahedra

Instructions available from Byriah Loper’s Flickr

 

Three Interlocking Irregular Hyperboloidal Parabitruncated Gyrobifastigia
Image source: https://www.flickr.com/photos/byriahloper/17416674009/

Three Interlocking Irregular Hyperboloidal Parabitruncated Gyrobifastigia

Instructions not available

 

Five Interlocking Irregular Hyperboloidal Dodecaugmanted Cuboctahedra v.2 (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/17367712645/

Five Interlocking Irregular Hyperboloidal Dodecaugmanted Cuboctahedra v.2

Instructions available from Byriah Loper’s Flickr

 

This next model is the most complex and time-consuming one he’s designed. It took 6 months to design this shape without using a computer!

Galaxy
Image source: https://www.flickr.com/photos/byriahloper/16360486394/

“Galaxy” Fifteen Interlocking Wrinkled Octahedra v.6

Instructions not available

 

Five Interlocking Irregular Hyperboloidal Dodecaugmented Cuboctahedra
Image source: https://www.flickr.com/photos/byriahloper/15124756636/

Five Interlocking Irregular Hyperboloidal Dodecaugmented Cuboctahedra

Instructions available from Byriah Loper’s Flickr

 

Five Interlocking Irregular Hyperboloidal Rhombic Dodecahedra (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/14517036970/

Five Interlocking Irregular Hyperboloidal Rhombic Dodecahedra

Instructions not available

 

"Event Horizon" Twenty Interlocking Irregular Augmented Tetrahedra (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/13913103465/

“Event Horizon” Twenty Interlocking Irregular Augmented Tetrahedra (Byriah Loper)

Instructions available in Mind-Blowing Modular Origami: The Art of Polyhedral Paper Folding

 

This next creation took almost 40 hours to fold and assemble out of 150 units!

Ten Interlocking Irregular Hyperboloidal Triaugmented Omnitruncated Digonal Dihedra (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/12237634405/

Ten Interlocking Irregular Hyperboloidal Triaugmented Omnitruncated Digonal Dihedra

Instructions available from Byriah Loper’s Flickr

 

"K5" Twenty Interlocking Tetrahedra v.2 (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/11825563785/

“K5” Twenty Interlocking Tetrahedra v.2

Instructions available in Mind-Blowing Modular Origami: The Art of Polyhedral Paper Folding

 

Twenty Interlocking Irregular Tetrahedra (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/8952536072/

Twenty Interlocking Irregular Tetrahedra

Instructions not available

 

Four Interlocking Irregular Triaugmented Quasidiminished Hexahedra (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/8717701791/

Four Interlocking Irregular Triaugmented Quasidiminished Hexahedra

Instructions not available

 

Five Interlocking Irregular Tetragonaly Twisted Triakis Tetrahedra v.2 (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/8248242802/

Five Interlocking Irregular Tetragonaly Twisted Triakis Tetrahedra v.2

Instructions available from Byriah Loper’s Flickr

 

"K7" Twenty Interlocking Snub Digonal Dihedra (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/7874723984/

“K7” Twenty Interlocking Snub Digonal Dihedra

Instructions not available

 

This incredible creation is folded out of 180 units!

Fifteen Interlocking Wrinkled Rhombic Prisms (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/24686550056/

Fifteen Interlocking Wrinkled Rhombic Prisms

Instructions not available

 

Eight Interlocking Tetrahedra #4 (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/27903077825/

Eight Interlocking Tetrahedra #4

Instructions not available

 

Thirty Interlocking Triangles (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/27785154803/

Thirty Interlocking Triangles

Instructions not available

 

This last model might be my favourite one. It’s folded and assembled from 120 units and reminds me of a Borg cube from Star Trek.

Thirty Interlocking Squares (Byriah Loper)
Image source: https://www.flickr.com/photos/byriahloper/28304595664/

Thirty Interlocking Squares

Instructions not available

 

If you want to see more you can check out Byriah Loper’s Flickr account.

He also has a book that’s available on Amazon if you’re feeling adventurous and you want to try folding some very difficult models.