How does your spine stack up? These vertebral stacking blocks fit together to form a three-quarter size spine model. A weird Halloween Party game perhaps?

See here for assembly video: https://youtu.be/z6MckyVLsLw 
 
This model is designed as an interactive way to learn basic spinal anatomy. If you are looking for a more robust display model, you might consider this design: https://social.thangs.com/m/60341.  If you are looking for a full-size model with more biomechanically accurate movement, you might consider this design: https://social.thangs.com/m/60245 

With the exception of C1 and C2, vertebrae are numbered on the posterior aspect of the vertebral body. The numbers are to assist with assembly and are hidden in the final assembled model. There was only space for numbers, so you’ll have to learn what C1 and C2 look like and be able to differentiate between cervical, thoracic and lumbar vertebrae. (It’s not that hard!)

Every effort has been made to maintain anatomical accuracy; however some small modifications were necessary to optimize the files for printing. In particular, the bone around the transverse foramen in the cervical spine, and the articular processes and lamina of the cervical and upper thoracic vertebrae have been thickened. 

Anatomically, the odontoid process of the C2 axis is held in place by the transverse ligament of the C1 atlas. In this model, the transverse ligament has been “ossified” leaving a hole for the odontoid process to click into place. This hole is intentionally tight to hold it in place. Expect to use a bit for force to snap them together, or file down the surfaces of the odontoid process as needed.

Male and female connectors have of course been added to each vertebral body.

Printing: 
This is an intermediate project that requires good skills in setting up supports and in post-print cleaning and preparation.

The vertebrae in the files are oriented upside-down to print on the flat surface of the male connector. You will need to set up supports for the rest of the vertebral body. Be especially careful when setting up supports for the downward-oriented superior facet joints. “Tree” supports in Cura work well.

Assembly:

There are some important considerations for post-print clean-up of this model. 

The fit between adjacent vertebra must be as tight as possible. Any movement between vertebra, especially the lower ones, will amplify up the spine and you will end up with an unstable spine with very poor posture!

When the pieces come of the print bed the first layer will be protruding out slightly, this is known as the “elephant’s foot.” If you try to connect the vertebra right off the print bed, this elephant’s foot will prevent the male piece from inserting. In order to achieve optimal fit, gradually file off the elephant’s foot while repeatedly attempting to connect the vertebra. As soon as you can forcefully insert the male piece, stop filing! The first few attempts to connect the vertebra should be very tight and difficult. After a few insertions, the surfaces will smooth out and you’ll be left with a nice tight connection.

Do not overdo the filing or you’ll be left with wiggly vertebrae!

Here are more of my anatomy designs you might enjoy:
Flexible Three-Quarter Spine Model with Display Stand: https://social.thangs.com/m/60341
Full Size Human Foot Model: https://social.thangs.com/m/60045 
Full Size Human Hand Model: https://social.thangs.com/m/60043 
Full Size 18-Piece Magnetic Human Skull Model: https://social.thangs.com/m/60036 
Full Sized Articulating Spine: https://social.thangs.com/m/60245
16-Piece Full Sized Brachial Plexus Model: https://social.thangs.com/m/47926 
6-Piece Magnetic Female Pelvis Model: https://social.thangs.com/m/60519 
Anatomically Correct Voronoi Heart: https://social.thangs.com/m/50472 
Pelvis Model with Adjustable Ball and Socket Joint: https://social.thangs.com/m/60546 
Novelty:
Happy Halloween Articulating Spine: https://social.thangs.com/m/27750 
Wearable Spine: https://social.thangs.com/m/27874
Custom Embossed Spine: https://social.thangs.com/m/32980 
Skull Jewelry Set: https://social.thangs.com/m/27766 
Vertebrae with Secret Compartment: https://social.thangs.com/m/363275 
Brain Teaser Puzzle: https://social.thangs.com/m/333304 
Tooth Dish: https://social.thangs.com/m/396068
Fingerbone Windchime: https://social.thangs.com/m/391916
Skull Windchime: https://social.thangs.com/m/391327
Skull Bulb (solid): https://social.thangs.com/m/377786 
Skull Bulb (Voronoi): https://social.thangs.com/m/377785 
Teeth Saucer: https://social.thangs.com/m/377781
Teeth Cup: https://social.thangs.com/m/377780
Architected Skull (hexagonal honeycomb): https://social.thangs.com/m/365051
Architected Skull (gyroid): https://social.thangs.com/m/365047 
Architected Skull (FCC): https://social.thangs.com/m/365043
Skull Ketchup Cap: https://social.thangs.com/m/362347 


Vertebral Stacking Blocks

Stacking Vertebrae Display only do not print.stl

If you’re bored of Lego, this 3D printed self-interlocking construction block will break your brain. It takes minutes to print, months to figure out!

See here for video for demonstrates of the concepts outlined below: https://youtu.be/j10wzy0qGOg 

Officially known as an “SL Block,” this octocube shape is part of a family of “topologically interlocking assemblies,” that is, shapes that hold together without the use of connectors or adhesives to form self-interlocking structures. Self-interlocking structures have interesting architectural and engineering applications.

A ends of a single “SL” block resemble an “S” and an “L.”. In assembly, SL blocks always occur in pairs, called a “Conjugate Pair.” In the pictures and video, conjugate pairs are shown with one white and one black piece.

Conjugate pairs lock together in six different ways, called “engagements,” to form “SL Strands.” Each type of engagement adds a unique translation or rotation to the SL Strand. The six types of engagements are denoted as “h,” “t,” “s,” “d,” “a” and “y.”

Using this system, the SL strands can be represented as strings consisting of six letters that stand for
the six types of engagements.


The first example in the video is an “h4” SL Strand. “h” engagements are straight with no rotations or translations, so the strand is straight.

The next example is an “a4” SL Strand. “a” engagements create a 90 degree rotation but no translations, so the “a4” strand makes a closed, cube-shaped structure.

The final examples in the videos show more complicated “(as2)4” and “(dth)4” strands. These modules can then be connected to form larger and increasingly complex self-interlocking structures.

Is your brain broken yet? Interested in learning more? Start here:
https://archive.bridgesmathart.org/2018/bridges2018-107.pdf


Brain Breaker Blocks

These two polyhedra are known as “Golden Rhombohedra” because the diagonals of the faces are the golden ratio. They combine and tile 3D space in ways that are complex and beautiful.

These files have inserts for magnets to make is easier to visualize and understand how they fit together.

These two polyhedra are part of a family of polyhedra known as the “golden isozonohedra.” There are only five golden isozonohedra. The “acute golden rhombohedron” and “obtuse golden rhombohedron” provide here are the most simple, but they can be combined together to form three more golden isozonohedra, the  “Bilinski dodecahedron”, the “rhombic icosahedron,” and the “rhombic triacontahedron.”

See here for video of finished pieces and demonstration on how they fit together: https://youtu.be/AQKMeJGCrfE

The files provided are for one version of the acute golden rhombohedron and two versions of the obtuse golden rhombohedron. Files are provided with or without supports.

The two versions of the obtuse golden rhombohedron are the same shape, but one has magnet holes on all faces, while the other has magnet holes on only half of the faces. Most of the obtuse golden rhombohedra end up on the outside of the final polyhedra and so don’t need magnets on the outside faces. This also helps cut costs in terms of number of magnets needed. Obtuse golden rhombohedra that are contained entirely within the larger polyhedra need to have magnets on all faces, but you’ll only need three of these.

To make all the five golden isozonohedra you will need:
10 acute golden rhombohedra
7 obtuse golden rhombohedra with magnets on three faces
3 obtuse golden rhombohedra with magnets on all faces

The magnet holes fit 1/8” by 1/16” cylindrical magnets. The polarity of magnets on each face must be facing opposite directions, and the pattern must be consistent on every face of every piece in order for all of the faces to snap together interchangeably. Magnets can be press fit with pliers, no glue needed.

The magnets used in the design and assembly of this model were purchased through www.kjmagnetics.com. 


Golden Rhombohedra 

Display only do not print.stl

This simple shape can be used create numerous complex and interesting 3D tilings and formations.

The parallelepiped is essentially an octahedron with two tetrahedrons attached to opposite faces, so the tiling is based on the octahedron and tetrahedron pattern found in an octet truss.

The holes are sized for 1/8" cylindrical neodymium magnets, 1/32" long. This size of magnet was selected for cost reasons and to minimize the repulsive forces between the magnets at each tip. This size of magnet is not very strong on its own but suffices when there are multiple faces joined together. If you choose to scale the model larger, you will want to use larger magnets. 

The six magnets at the two tips are all inserted with the same polarity, the remaining six magnets around the center are inserted with opposite polarity.
It is a good idea to clean the holes out first with a 1/8" drill bit. CA glues works well.
See here for a video on how to assemble the first and second level cuboctohedron: https://youtu.be/Fpc0BToJeA0 

The first level cuboctohedron is made with 12 individual parallelepiped shapes, the second level cuboctohedron is made with 36 individual parallelepiped shapes


Magnetic Parallelepiped Blocks

This simple shape can be used create numerous complex and interesting 3D tilings and formations.
The parallelepiped is essentially an octahedron with two tetrahedrons attached to opposite faces, so the tiling is based on the octahedron and tetrahedron pattern found in an octet truss.
The holes are sized for 1/8" cylindrical neodymium magnets, 1/32" long. This size of magnet was selected for cost reasons and to minimize the repulsive forces between the magnets at each tip. This size of magnet is not very strong on its own but suffices when there are multiple faces joined together. If you choose to scale the model larger, you will want to use larger magnets.
The six magnets at the two tips are all inserted with the same polarity, the remaining six magnets around the center are inserted with opposite polarity.
It is a good idea to clean the holes out first with a 1/8" drill bit. CA glues works well.
See here for a video on how to assemble the first and second level cuboctohedron: https://youtu.be/Fpc0BToJeA0 
The first level cuboctohedron is made with 12 individual parallelepiped shapes, the second level cuboctohedron is made with 36 individual parallelepiped shapes


When bubbles connect together to make foam they take on a complex structure known as the “Weaire–Phelan structure.” Some of the bubbles become 12-sided pentagonal dodecahedra (PD), other bubbles become 14-sided tetrakaidecahedra (TKD). These bubble blocks let you see how the different shaped bubbles connect and create “foam” structures.
To start building, you will need to print a few of the “PD” and “TKD 4 tab” files. Once you start building with these, you will notice that the outward facing surfaces of the “TKD 4 tab” blocks have visible connecting tabs. If you would like to have a smooth, foam-like outer surface, print of some of the some of the other TKD files that only have one, two of three tabs. This will allow you to have a smooth other surface.
See here for video: https://youtu.be/QChSuaVTFSA 
When setting up supports for these, be sure that you support the lower edge of the tabs. You will need to do some post-print clean-up. If you find that the snaps are too tight to connect, simply file down the edges of the tabs until you achieve the desired fit. 
Expect to do some post processing to smooth the edges of the snap surfaces.
There is a good introduction to the “Weaire–Phelan structure” here: http://www.steelpillow.com/polyhedra/wp/wp.html 


Bubble Blocks

PD.stl

These interconnecting “tube-like” pieces offer a tactile way to explore and discover the geometry of the 12-sided dodecahedron and 20-sided icosahedron, two dual Platonic polyhedra. 

See video here: https://youtu.be/SR5kkRHFiGo 

Pieces snap together at a 90-degree angle. The connecting surfaces of the “Penta Tube” align with the edges of a regular pentagon. The angles of the connecting surfaces of the “Dihedral Tube” are derived from the dihedral angle of the dodecahedron, that is, the angle between two adjacent faces of a dodecahedron. The “End Cap” is an aesthetic option for putting on unused ends.

The primary structure that can be made using these pieces is a basic dodecahedron using 12 “Penta Tubes” and 30 “Dihedral Tubes.” This is the spherical structure pictured above. The “Penta Tubes” become the faces of the dodecahedron, while the “Dihedral Tube” is oriented orthogonal to the edge of the dodecahedron and holds adjacent faces at the proper dihedral angle.

Try changing the orientation and positioning of the pieces and you’ll discover even more polyhedra based on the dodecahedron and icosahedron.


Penta Tubes

PentaTube Display Only Do not print.stl

These Tangled Tubes will infinitely tile 3D space and form all sorts of interesting patterns.

Put a bowl of them on your coffee table for your friends to ponder!

See here for video on one way that 24 pieces can fit together: https://youtu.be/9gYk9i9vArM

The end faces of the four joined tubes are congruent to the faces of the tetrahedrons and octahedrons in an isotropic vector matrix. The faces of the short tubes are congruent with the octahedron faces, while the longer tubes are congruent with the faces of the adjacent tetrahedrons.

Print out two “Tangled Tubes half” and one “Tangled Tubes Connector” for each piece. Join the two “Tangled Tubes half” pieces together with the “Tangled Tubes Connector” to ensure proper alignment of the faces and secure with a dab of CA glue.

The “Tangled Tubes Display” file is provided for reference only and is not intended to be printed.

The holes accept 3mm x 3mm  or 1/8”x1/8” cylindrical magnets. It is a good to clean the holes out with a 1/8" drill bit to remove and burrs or imperfections prior to inserting the magnets. Polarity of the magnets should be opposite for the short and long ends of the tubes. Secure magnets with a dab of CA glue.


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Vertebral Stacking Blocks

Brain Breaker Blocks

Golden Rhombohedra

Magnetic Parallelepiped Blocks

Bubble Blocks

Penta Tubes

Tangled Tubes