Archimedean Solids

TurboSquid 3D geometric models

Tuesday, 31 May 2022 by Bruce Rawles

Fellow geometer, 3D animator, techno-nerd, mystic, and life-long friend, Dave Van Dyke alerted me to some examples of very cool 3-dimensional models using TurboSquid (3D Models for Professionals) a couple of days ago. The links below connect with a small set of the many examples of 3-d geometric models – some free, others inexpensive – all gems, especially considering the “labor of love” efforts put into these detailed models! Going beyond geometric constraints, you have orders of magnitude more to explore! They can be downloaded and adapted wherever your imagination might lead! Here are some samples to pique your interest!

polyhedron made of inter-locking blue squares

geodesic polyhedra (truncated icosahedra); small and large sizes connected at vertices

polyhedron made of interlocking blue triangles — polyhedron made of inter-locking blue triangles

icosa-dodeca-geometric model with wavy extruded interconnecting struts

SMAs in SMA (SMA-ll stellated dodecahedra in San Miguel de Allende)

Thursday, 5 May 2022 by Bruce Rawles

¡Feliz Cinco de Mayo! Last week, my wife Nancy and I enjoyed a long-overdue, much-needed getaway/vacation and chose San Miguel de Allende, Mexico, a place we’d heard great things about for decades from numerous sources. We very much enjoyed our immersion into the culture, cuisine, and art that this historic city is known for. In addition to world-class dining, lots of “heart decor” and so much more, I was amazed at how many 3D geometric stars were present in this lovely city, both in numerous shops and even in permanent street art! Since artsy stars, wings, and hearts are here in abundance, there are plenty of stellated polyhedra, but the predominant variety seemed to be one of my favorite shapes, the small stellated dodecahedron (one of the four Kepler–Poinsot polyhedra) which I’ve featured in numerous places on this website. I mentioned (in my broken Spanish, resurrected from high school classes a half-century ago) to a few of the shopkeepers that a foldup version that would fit in a tourist’s suitcase might afford more sales, since shipping these lovely fabrications is probably a bit expensive.

If you want to make your own (I suggest trying in cardboard first) here’s a foldup pattern from page 219 of Sacred Geometry Design Sourcebook; you’ll want to make 6 copies of this page. Join the two edges labeled 1 and also join the two edges labeled 2. If you fold together just one copy of this page, you’ll get a double pentagonal pyramid, which is another interesting shape. However, if you fold up the 2 pentagonal pyramid halves, crease the middle shared edge, and fold the other direction, you’ll have 1/6 of what you need to make this classic shape. MC Escher fans will probably recall this classic image.

Small Stellated Dodecahedron fold-up pattern from page 219 of Sacred Geometry Design Sourcebook - Universal Dimensional Patterns by Bruce Rawles — Small Stellated Dodecahedron fold-up pattern from page 219 of Sacred Geometry Design Sourcebook – Universal Dimensional Patterns by Bruce Rawles

I’ve included an assortment of photos from this trip below, including a few other familiar geometries you’ll probably recognize; enjoy! For many more photos of our San Miguel de Allende, Mexico trip this past week, visit my personal Facebook page.

Small Stellated Dodecahedra hanging from the ceiling of the gazebo in the centro park adjacent to the Parrochia church, San Miguel de Allende, Mexico — Small Stellated Dodecahedra hanging from the ceiling of the gazebo in the Centro park adjacent to the Parrochia church, San Miguel de Allende, Mexico

cluster of brass Small Stellated Dodecahedra; San Miguel de Allende, Mexico

Small Stellated Dodecahedra and many other colorful artsy decorative items in another street vendor shop; San Miguel de Allende, Mexico

Small Stellated Dodecahedron -hanging in a restaurant interior courtyard; San Miguel de Allende, Mexico

street vendor photo: metal small stellated dodecahedra and other art objects; San Miguel de Allende, Mexico

metal stellated polyhedra decorating trees in an interior courtyard; San Miguel de Allende, Mexico — metal stellated polyhedra (one of many polyhedra) decorating trees in an interior courtyard; San Miguel de Allende, Mexico

metal stellated polyhedra; San Miguel de Allende, Mexico

interior of a metal stellated polyhedron; San Miguel de Allende, Mexico

Small Stellated Dodecahedra and other geometric lamps; street vendor lamp shop; San Miguel de Allende, Mexico

large metal small stellated dodecahedron on street corner 1 block south of Parrochia church; San Miguel de Allende, Mexico — daytime photo of a large metal small stellated dodecahedron on the street corner one block south of Parrochia church, San Miguel de Allende, Mexico …

… the same large metal small stellated dodecahedron casting light on the street corner at night; San Miguel de Allende, Mexico

courtyard art: large stellated cube; San Miguel de Allende, Mexico

reflecting sphere art in hotel lobby; San Miguel de Allende, Mexico — reflecting sphere art in a hotel lobby; San Miguel de Allende, Mexico

Other examples of small stellated dodecahedra from this website:

sculpture by Gregory Hoag of I-Connect (formerly Metaforms).

zometool stellated dodecahedron — zometool construction (the outer blue shape is a small stellated dodecahedron)

New Frontiers of the Gold Country - logo

Martineau Solar System Calendars again available; still 9 months left in 2022!

Friday, 1 April 2022 by Bruce Rawles

OK, I’m a bit late (by about 4 months from when I usually update these), but there are still nine months left in the year 2022 to enjoy these lovely calendars! Freshly updated, these timeless images that portray amazingly accurate geometric representations of the planetary orbits in our very own solar system are now (again) available in printed calendar form!

Martineau Solar System Calendars

These 12 images are highly accurate geometric models of our solar system; details here. They were inspired by the remarkable work of John Martineau (publisher of Wooden Books), who wrote “A Little Book of Coincidence”. Tiled images of planetary surfaces and related images form the backgrounds. Images are two or more orbits defined by simple 2D (circles, triangles, squares, pentagons, hexagons, octagons) or 3D geometries (e.g. tetrahedron, icosahedron, dodecahedron) typically with 99.9% or greater accuracy. The work picks up where Johannes Kepler’s mystical exploration left off. A newly revised calendar (which is updated every year) with images from the Martineau Solar System is again available for 2022.

Educational Books and Toys: RedHen Update!

Tuesday, 28 December 2021 by Bruce Rawles

It’s been a while since we featured RedHen Books and Toys with their unique assortment of hard-to-find educational materials, toys, games, and books such as Bradford Hansen-Smith’s circle folding videos, books, and supplies, Zometool, Froebel gifts, and much more! For math or geometry teachers, homeschoolers, or anyone enthused about the study and practice of geometry – or wanting to propagate that enthusiasm – Red Hen has an excellent selection for kids spanning a wide age range.

To get a sense of the generous variety of available products, I would suggest clicking on the “All Items” link in the Red Hen website left sidebar, and then scrolling through a page at a time to not miss any of the unique and interesting items; the samples below are just a small handful of what you’ll find! Here are a few of the many unique items that make great gifts or educational catalysts year-round. I’m a huge fan of Zometool! Spirograph was a big positive influence in my childhood a half-century ago, so I’ll feature those two first. Enjoy!

Zome Crystallography kit

Spirograph Design Tin Set

Geometric Coloring Cards

Kaleidograph Flora

Rolligo

Mathematics with Geoshapes

Archimedes Square Stomachion puzzle

Fold a Soccer Ball

Tetrahedron Octahedron Cube poster

3-D Polyhedra Software: Modeling, Art, Animation, Apps and more

Monday, 28 September 2020 by Bruce Rawles

If you want to experiment with 3D geometry software, check out Stella from Software3D; lots of possibilities here including the nets (a.k.a. fold-up patterns) for making polyhedra cut out from flat material, such as paper, cardboard or whatever. The animations showing the flattened 2-dimensional nets morphing into their completed 3-dimensional counterparts are particularly fun and useful since you can see intuitively how these polygons all work together to make a whole greater than the sum of its parts. :-)

Among the many other helpful and interesting products and items on this site is the “Worlds Kaleid!” live camera kaleidoscope app for Android.