### Sand Snowman Paperweight Toy

Similar sand toys available here:

From Amazon: **BUY NOW: Sand Paperweight Toy**s

Sand Holiday Paperweight Toy: physics of granular materials- matter with unique properties between those of solids and liquids- as demonstrated with this simple toy. Granular materials, such as the sand in this toy, flow but also stack with a characteristic “angle of repose” as can be seen here as pyramid like ridges that form over the images of Santa and winter wonder.

### CMY Platonic Solids

Available from these sources:

From Amazon: **BUY NOW: CMY Cube, CMY Octohedron**

From CMY Cubes: **Platonic Solids**

Check out this nice set of Platonic Solids gaming dice

CMY Platonic Solids: The five famous convex regular polyhedra with thin film coatings, Cyan, Magenta, and Yellow, that allow filtering of the light that enters or leaves particular facets of each acrylic prism. I was struck by the intricate patterns produced in each object’s shadow by the refracted light- especially as the objects rotate.

### Platonic Solids Dice Set

Get this nice set of regular polyhedra dice here:

From Etsy: **BUY NOW: Polyhedra Dice Set**

Less expensive sets of standard plastic dice here:

From Amazon: **BUY NOW: Polyhedra Dice Set**

Platonic Solids Dice Set: The five famous convex regular polyhedra in the form of fair dice. This set is cast in metal with clean edges and makes for a great way to own these symmetrical objects that have fascinated thinkers ever since the ancient Greeks wrote about them circa 360 BC. Only these five forms meet these criteria (in 3D space) for each face: must be equal in size, be equal in number of sides, each side of equal length, identical in angle were any two sides meet, and have the same number of sides meet at each vertex point of the solid. 2000 years later the famous mathematician Euler determined that for these 5 shapes V-E+F=2, the number of corners (vertices), minus the number of edges, plus the number of faces, will always equal 2.

### The Holoscope : Icosahedron

Order a holoscope from the artist's gallery here:

The artwork of Gary Allison: **BUY NOW Holoscopeworld.com **

Look through other holoscopes in my collection here: Holoscope Kaleidoscopes

The Holoscope Icosahedron: the intricate beauty of multiple internal reflections from 20 triangular mirrors in the shape of this famous platonic solid. The interior is viewed from one corner and illuminated by light entering from glass spheres placed at all of the other 11 vertices. A type of kaleidoscope based on mirrored polyhedra by artist Gary Allison, (swipe to see the dodecahedron and cube) and future posts will include tetrahedron and octahedron holoscope forms as I complete my Platonic solids set. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.

### Scutoids

This set of 3D printed scutoids available here:

From Etsy: **BUY NOW: Scutoid container set**

Scutoids: a recently recognized form of geometric solids discovered in 2018. Scutoids have a different polygon on each end, and when packed together maximize stability and minimize energy when forming a boundary layer- such as the membranes around organs in living tissue. These 5-6 scutoids have pentagons on one end and hexagons on the other. Discovered by a collaboration of biologists and mathematicians in 2018, this set is sold by Recep Mutlu of 3DPrintBase.

### Ferromagnetic Elements

10mm cubes of 99.9% pure elemets available here:

From Luciteria: **BUY NOW: Pure Element Cube Samples**

These cubes include a laser etching of the symbol and element name on each.

The main 4 ferromagnetic elements are: Fe, Co, Ni, and Gd.

Ferromagnetic Elements: which metals from the periodic table experience strong attraction towards a magnet? Here are seven samples- 1 cm cubes of 99% pure elements: Ti (titanium), Fe (iron), Co (cobalt), Ni (nickel), Cu (copper), Gd (gadolinium), and W (tungsten)- which of these metals are ferromagnetic? Swipe once to check your answer, swipe twice to see how some are more strongly ferromagnetic than others. Although magnets are familiar objects, the physics of ferromagnetism is very complex and is described by the quantum mechanics of intrinsic particle spin and the specific electron configurations of solids and molecules.

### Holoscopes: Dodecahedron and Cube

Order a holoscope from the artist's gallery here:

The artwork of Gary Allison: **BUY NOW Holoscopeworld.com **

Look through other holoscopes in my collection here: Holoscope Kaleidoscopes

Holoscopes: polyhedra of mirrors (dodecahedron and cube) with the interior viewed from one corner and illuminated by light entering from glass spheres placed at all of the other vertices. A type of kaleidoscope based on mirrored polyhedra by artist Gary Allison @holoscope2000, and future posts will include tetrahedron, octahedron, and icosahedron holoscope forms as I complete my Platonic solids set. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.

### The Holoscope: Cube with Spheres

Order a holoscope from the artist's gallery here:

The artwork of Gary Allison: **BUY NOW Holoscopeworld.com **

The Holoscope: a cube of mirrors with the interior viewed from one corner and illuminated by light entering from glass spheres at the other seven vertices. A type of kaleidoscope based on truncated Platonic solids by artist Gary Allison. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.

### 12-Faced Holoscope

Order a holoscope from the artist's gallery here:

The artwork of Gary Allison: **BUY NOW Holoscopeworld.com **

12-Faced Holoscope: a dodecahedron of mirrors. A type of kaleidoscope based on truncated Platonic solids by artist Gary Allison. This holoscope is in the form of a dodecahedron with each corner cut off allowing light to enter through triangular holes. Through the symmetry of the reflections, these triangles appear as an infinite array of tetrahedrons. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.

### Oloids: Solid and Anit-oloid

Order your Anti-Oliod today: available in three types of metal:

From The Matter Collection: **ORDER NOW: Anti-Oloids in Brass, Copper, and Steel **

Oloids: “solid hull” and “ruled surface” types made from brass and copper- oloids are unique solids that roll in such a way that every point on their surface comes in contact with the plane. The basis of the oliod’s geometry is that of two connected circles, one perpendicular to the other such that the rim of each circle goes through the center of the other. The shapes you see here are the results of connecting the rims of these circles together with a family of straight lines, one method leads to the solid convex hull form, and another way leads to the ruled oloid (anti-oloid).

### Sand Triangles Kinetic Toy

This vintage toy is no longer in production (I found this on on eBay). Here are some sand sculptures that also depend on the angle of repose of the granular medium used:

From Amazon: **BUY NOW **

Sandscape Sculptures

Sand Triangles Kinetic Toy: physics of granular materials- matter with unique properties between those of solids and liquids- as demonstrated with this simple, oddly satisfying, vintage item by Naef Toys. Granular materials, such as the sand in this toy, flow but also stack with a characteristic angle of repose as can be seen here- the triangular peaks that form always have the same peak angle. The angle of repose mostly depends on the shape of the individual grains, rounded pieces cannot stack as steeply as rough shaped ones.** **

### Volumes of Constant Width

Get a set of Reuleaux solids here:

From Shapeways: **BUY NOW Volumes of Constant Width **

Volumes of Constant Width: these shapes have constant diameter no matter their orientation and will roll like spheres between two planes- note how the acrylic plate stays parallel to the table top. Two of these three solids are based on the Reuleaux triangle and the other on a Reuleaux pentagon.

### Hexa Sphericon

Sphericon and Hexa-sphericon: order your set today!

From the Matter Collection:** BUY NOW The Sphericon (Hex and Regular) **

Hexa-Sphericon: Sphericons are unique solids that roll in such a way that every point on their surface comes in contact with the plane. Solids from the sphericon family all have one side and two edges. Each sphericon is based on a regular polygon, with the basic sphericon derived from a square, and here- a more interesting case with more complex rolling motion- from a hexagon.

### Hexa Sphericon

Sphericon and Hexa-sphericon: beautiful works of art in metal- available here!

From the Matter Collection:** BUY NOW The Sphericon (Hex and Regular) **

3D printed as well as handmade sphericons and similar shapes avaiable here:

From Etsy:** BUY NOW: Sphericons **

Hexa-Sphericon: Sphericons are unique solids that roll in such a way that every point on their surface comes in contact with the plane- following the path shown here with white paper. Solids from the sphericon family all have one side and two edges. Each sphericon is based on a regular polygon, with the basic sphericon derived from a square, and here- a more interesting case with more complex rolling motion- from a hexagon.

### Sand Paperweight Toy

Available from these fine sources:

From Amazon:** BUY NOW Sand Globe Toys **

From Amazon:** BUY NOW Sand Globe Toys: Winter Theme**

A common version of this toy is for football fans:

From eBay: **BUY NOW Sand Football Paperweight Toy **

Wikipedia has a nice introduction to the amazing world of granular material science

Sand Paperweight Toy: physics of granular materials- matter with unique properties between those of solids and liquids- as demonstrated with this simple toy. Granular materials, such as the sand in this toy, flow but also stack with a characteristic “angle of repose” as can be seen here as pyramid like ridges that form over the images of penguins.

### Holoscopes

Order a holoscope from the artist's gallery here:

The artwork of Gary Allison: **BUY NOW Holoscopeworld.com **

6 and 12 Faced Holoscopes: a cube and dodecahedron of mirrors. A type of kaleidoscope based on truncated Platonic solids by artist Gary Allison @holoscope2000. These holoscopes are in the form of two famous Platonic solids- each with all the corners cut off to allow light to enter through triangular holes. Through the symmetry of the reflections, these triangles appear as an infinite array of tetrahedron shapes in the dodecahedron, and as beautiful repeating stellated octahedrons in the cube. Each holoscope has stained glass on the exterior and front surface mirrors on the inside which create the amazing and seemingly impossible spaces within.