iiinova — where your digital self keeps evolving

Paula Beardell Krieg @paulakrieg.bsky.social · 22/08/2026

I appears That I might be living in my own marvelous word problem. This year my raspberry patch is magnificent, but it’s been too early for berries. I’d get astray one here and there, but three days ago I found three ripe ones. Yesterday there were 9. Today, almost 27!

Today’s harvest of raspberries. I seem to be on track to getting about 3 to the power of x berries per day. To be continued.

Raspberries forming a heart… showing ypu how much I love my raspberries. Will save these for breakfast.

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Paula Beardell Krieg @paulakrieg.bsky.social · 28/07/2026

A blog post with elementary teachers in mind bookzoompa.wordpress.com/2026/07/27/p...

A wildly colorful frame made of black paper and geometric shapes arranged to make a striking border for a drawing of a little chick.

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Paula Beardell Krieg @paulakrieg.bsky.social · 16/06/2026

Forgive me for pointing you to a post that I wrote 6 years ago, but reading my impressions of Ben Orlin‘s new book gave me such pleasure today that I wanted to share. bookzoompa.wordpress.com/2020/01/03/m...

bookzoompa.wordpress.com

My First Read of the New Decade

The first book I’m reading this decade is a beautiful object. I am so taken by the design of this book that I am asking your forgiveness, as I will barely be referencing the contents of the b…

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Paula Beardell Krieg @paulakrieg.bsky.social · 15/05/2026

About a month ago MoMath let me guide over 100 of their museum goers in making a tetrahedron in a cube in a rhombic dodecahedron, inspired by a drawing in Kepler's notebook. Here's the video playlist of the project, which points towards all the nets that we used. www.youtube.com/playlist?lis...

A tetrahedron that fits precisely and surprisingly into a cube. This is a image from Johannes Kepler's notebook, 1619

A Rhombic Dodecahedron with a cube inside, which houses a tetrahedron.

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Paula Beardell Krieg @paulakrieg.bsky.social · 30/04/2026

When you start looking for simple and enjoyable end of the year activities, remember that it’s always satisfying to make a box. Here’s a nice one. youtu.be/FgI5l6EBzuM?...

youtu.be

Cube Box to Make, with wings instead of tabs, cut, score and glue

YouTube video by Paula B Krieg

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Paula Beardell Krieg @paulakrieg.bsky.social · 23/03/2026

Last year, dashing out to a family gathering, I managed to put up a post about making this sweet little origami basket. Looking it over again, I like how, besides folding, it's also about how to work with paper. Such fun to make, to have and to give away. bookzoompa.wordpress.com/2025/04/19/o...

A small, colorful origami basket, just the right size to hold an egg, or candy, or even a handful of crayons.

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Reposted by Paula Beardell Krieg

John Golden @johngolden.bsky.social · 11/03/2026

#makeart www.joshuawcotter.com/words/make-art

joshuawcotter.com

Make Art — Joshua W. Cotter

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Paula Beardell Krieg @paulakrieg.bsky.social · 27/02/2026

Can’t resist aharing today’s wordle Wordle 1,714 2/6* ⬜🟩🟩🟩⬜ 🟩🟩🟩🟩🟩

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Paula Beardell Krieg @paulakrieg.bsky.social · 24/02/2026

Am teaching a class right now in which we construct cubes then alter them... Reminds me of the math concept of parents functions which are altered. We then combine the truncated and pierced cubes in fun ways. #mathart #paperengineering

Paper cubes which have been truncated, pierced and altered in various ways. Some of the negative spaces have been reconstructed.

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Paula Beardell Krieg @paulakrieg.bsky.social · 14/02/2026

Happy Valentines Day. Made this in 2018, and still love it. Loving Triangles.

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Paula Beardell Krieg @paulakrieg.bsky.social · 28/01/2026

Artist @hakoyamaho post models and their nets on Instagram. This one of golden ratio proportioned prisms caught my eye. Makes a cool pedestal for my Minnesota themed octahedron and for a small wooden sculpture by my husband.

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Paula Beardell Krieg @paulakrieg.bsky.social · 27/01/2026

I've been hearing from blog readers, in comments and DMs, who have lived in Minnesota, but who are not there now, It's touching how much they appreciate having something to make that honors their connection to the state.

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Paula Beardell Krieg @paulakrieg.bsky.social · 26/01/2026

Heartbroken over the events of the past few days. For my Minnesota friends, here is an Octahedron decorated with the color of your flag and your North Star motif. PDF on my blog post bookzoompa.wordpress.com/2026/01/26/s...

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Paula Beardell Krieg @paulakrieg.bsky.social · 25/01/2026

If the events of the day feel unbearable, I offer a bit of geometry to help you feel grounded. Here's a PDF to make some octagons. drive.google.com/file/d/1bOJ5... Print on card weight paper if you can, glue neighboring tabs together, add string before closing up. #mathart #octahedron #Healing

Octagons ornaments with heart decorations, sending out some love in the world. From me to you

Octagon ornaments hanging in my favorite coffee shop.

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Paula Beardell Krieg @paulakrieg.bsky.social · 22/01/2026

What bothers me about Archimedean Solids is that I can't visualize the part that was removed from the Platonic parent shape. Here's a solution for the cuboctahedron: build the Platonic Solid parent cube around it and notice the shape of the negative space+

The Archimedean Solid cuboctahedron. Although its Parent Platonic solid can be either a cube or an octahedron, I'm looking just at the cube derivation.

The cube around the cuboctahedron splays open for maximum exposure

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Paula Beardell Krieg @paulakrieg.bsky.social · 18/01/2026

I super like making models that illustrate simple concepts that are hard to grasp with words or in pictures, but which are easily grasped when seen in 3D. I've been pondering how to make a good model that show dual polyhedra, starting with the cube and octahedron. finally got it.

Cube, nicely splayed to reveal an octahedron whose vertices are the mid points of the faces of the cube.

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Paula Beardell Krieg @paulakrieg.bsky.social · 13/01/2026

Using pattern blocks motifs on larger pattern block shapes, in different arrangements. #patternblocks #symmetry #paperconstructions #triangles +

Refection of a triangle, which,together , glide

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Paula Beardell Krieg @paulakrieg.bsky.social · 09/01/2026

I guess I'll never stop playing with #blocks. Did some hand drawing on a large sheet of Canson paper, then used the paper to make blocks. There was one face that I like enough to digitally reproduce then apply it to a cube net applying done #symmetry actions.

Blocks with a single design reproduced on all faces.

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Paula Beardell Krieg @paulakrieg.bsky.social · 02/01/2026

Here's a hexagonal antiprism joined with a hexagon prism. Worked this out in anticipation of an upcoming zoom class at Canadian Bookbinders and Book Artists Guild - Book Arts: Realm of Solids 2026WKSP-01-13 share.google/709E8iib8Zbb... Turns out it's kind of perfect for housing scrolls.

The frontal view of a box made from a prism and antiprism joined together. Bright geometric designs on black.

View of a hexagonal Prism/antiprism box with bright geometric designs on black.

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Paula Beardell Krieg @paulakrieg.bsky.social · 30/12/2025

Thank you @johngolden.bsky.social Your reach is far greater than mine! I will Zoom teaching an introduction to solids class for the Canadian BookBinders and Book Artists Guild in January www.cbbag.ca/event-6403035

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Paula Beardell Krieg @paulakrieg.bsky.social · 30/12/2025

Been having a good old time constructing pattern block shapes and then adding designs to the faces. Here's a peak at me pushing them around to see what happens: youtu.be/ss_w0CiQuCY #symmetry #patternblocks #geometry #rhombicPrism #rhombus #bluepatternblock #mathart

Double wide pattern block decorated with symmetrical patterns, flanked by a couple of single wide pattern blocks.

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Paula Beardell Krieg @paulakrieg.bsky.social · 29/12/2025

Thinking about my Rhombus-playmate Malke Rosenfeld this holiday season. We put our heads together on many projects. Loved how she played with rhombi. Miss having her energy in the world. Here's a writing up from 2015, includes links to some of her pages. bookzoompa.wordpress.com/2015/03/31/p...

bookzoompa.wordpress.com

Piecing Together a Project, Over Land and Sea

This story begins in a teachers’ lunchroom, a couple of years ago, in Upstate NY. I was sitting with some teachers when another member of the staff started talking to a first grade teacher, M…

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Paula Beardell Krieg @paulakrieg.bsky.social · 19/11/2025

Playing around with irregular pentagons that I described in my previous post, doing reflections. #mathart

Two irregular pentagons joined at their 90 degree angle edges

Another arrangement of irregular pentagons joined at their 90 degree edges from the base and 60 degree angles joined together at the top

Two irregular pentagons joined to look like a butterfly

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Paula Beardell Krieg @paulakrieg.bsky.social · 19/11/2025

I've been making paper constructions of pattern blocks, then decided to add some extra ones to the traditional set. I'm particularly proud of this irregular pentagon. Even though I worked this out according to my own agenda, it's characteristics are so cool that I have no doubt that it's a shape +

Irregular pentagon that plays well with other pattern blocks.

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Paula Beardell Krieg @paulakrieg.bsky.social · 17/11/2025

Designed and taught a workshop based on constructing and decorating pattern blocks. Decided to include a few extra pieces, like the pentagon and irregular pentagon. Prior to decorating, oved howdelighted people were when I pointed out the relationship between stars and any five sided shape.

Paper constructed prisms of irregular pentagon, regular pentagon, triangular prism, along with a wooden pattern block. The decorative faces of the prisms relate to the edges of the faces, which , in the case of the pentagonal faces, start by finding the five pointed star that is created by connecting every other vertice until the star emerges.

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Paula Beardell Krieg @paulakrieg.bsky.social · 15/11/2025

Been teaching a flurry of polyhedron-related classes to artists, revisiting some favorite forms, like chiral boxes with deep diagonal pockets that @simon-gregg.bsky.social pointed me towards years ago, and the Liu Hiu solids via Jen Silverman www.jensilvermath.com/presentation... #mathart #mtobs

Yangma Tetrahedrons and the origami box that seems like its too small to hold them

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Paula Beardell Krieg @paulakrieg.bsky.social · 11/11/2025

Something else to do with a cube. Done with 300lb watercolor paper. Thinking outside and inside the box.

Three colorful cubes , two of which are sliced and pierced so that they have windows and protrusions. Very silly.

A lonely little cube, all dressed up with decorative swirls and windows which offer a glimpse within.

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Paula Beardell Krieg @paulakrieg.bsky.social · 19/10/2025

Lately I've been up to my ears in pattern block inspired forms. Been enlarging them for boxes, using their interior spaces & fractally decorating. The Jaffe Center has slipped me into their November schedule to teach a one session evening class with these forms. jaffecollection.org/workshops/fr...

Two triangles based on pattern blocks, and , oh my, looks like one of them opens up to reveal a little blue person getting some sunshine.

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Paula Beardell Krieg @paulakrieg.bsky.social · 01/09/2025

A post about the cubes I've been making bookzoompa.wordpress.com/2025/08/31/d... #mathart

Three cubes sitting around looking quite satisfied with themselves and each other. A mostly orange cube has designs influenced by Seminole Patchwork, a Native American invention. A black and white cube started with an Islamic Geometry construction, was generalized by John Golden in Geobebra, and then I messed with it in Adobe Illustration, and then there's a Rainbow cube that splits apart to reveal a secret hexagon or two.

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Paula Beardell Krieg @paulakrieg.bsky.social · 31/08/2025

Been working on some fun cubes this week. Taking patterns I've created then using them on cubes that are sliced in ways that allow them to interact. Because the patterns I make are inspired by so many different sources I think of them as Diversity Cubes. Nice box too. #mathart #patterns #cubes

There's a sliced cube that shows off the hexagon face embedded in its center; a cube that has the marbling on it reminiscent of Turkish techniques; the orange cube echoes Seminole Patchwork, and there's some references to Islamic geometry in he black and white cube.

Oh I didn't mean to include so much of the inside of my house in this photo, but oh well. Here's another arrangement of the cubes. A colorful tower.

Boxes are so challenging to get right and so satisfying to make. So much math goes into making a box. Let's teach more box making. Here are the nets for my box and lid. They make a handsome pair.

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Paula Beardell Krieg @paulakrieg.bsky.social · 25/08/2025

Another way to fill the rhombic dodecahedron happens to be the convex hull of a compound of an octahedron cube. #convexhull #polyhedron #compoundpolyhedra #rhombicdodecahedron #cube #octahedron

Three compounds of an octahedron and a cube sitting on my desk waiting for me to walk in this morning and admire them. That's a rhombic dodecahedron box to the left, which is the perfect fit for these solids.

Another view of these compound solids. The one made from a single pattern doesn't show off the compound-ness as well as the one on the right, but , really it's a satisfying shape even if you don't know or care about compound solids.

Oops. The cube lost its octahedron protrusions.

The blue patterned compound of the cube and the tetrahedron has hopped into its convex hill, the rhombic dodecahedron box while the cube looks on surrounded by the wayward points of the octahedron.

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Paula Beardell Krieg @paulakrieg.bsky.social · 24/08/2025

Unlike @davidkbutler.bsky.social , who fills up space with #rhombicdodecahedrons, I've been filling up the space within this shape. A hollow cube and a deconstructed cube work just fine to fill it. Blog post coming soon. I hope.

There's a hungry solid blue shape called a rhombic dodecahedron which wants to gobble up everything else in this photo.

The hollow orange cube consumes the little book, then the blue shape, which from some vantage points looks like a cube, turns itself inside out and wraps itself all around the orange cube.

Oh my. Now the fully filled up blue patterned shape slips perfectly into the blue box

Now both the cubes and the little book are neatly tucked into this twelve sided shape with rhombic faces.

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Paula Beardell Krieg @paulakrieg.bsky.social · 21/08/2025

So many people sent me yesterday’s NYT article on blossom fold that I couldn’t resist making one. Very pretty in three dimensions

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Paula Beardell Krieg @paulakrieg.bsky.social · 19/08/2025

Unintentionally I typed a 3 into the my search bar, so, naturally, AI defined it for me. It started with "AI Overview The number 3 is a fundamental number with various mathematical, cultural, and symbolic meanings. It is the third smallest prime number, and the first odd prime number" So then...

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Reposted by Paula Beardell Krieg

Christopher Danielson @triangleman.bsky.social · 12/08/2025

On my own this evening, this was about a half hour of work. We're gonna crush this thing!

Nine large hexagons, made of colorful pattern blocks with various and interesting symmetries, tiled together to make a larger mosaic, roughly 12 inches square.

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Reposted by Paula Beardell Krieg

Michael Pershan @mpershan.bsky.social · 11/08/2025

Hey check this out!!

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Paula Beardell Krieg @paulakrieg.bsky.social · 08/08/2025

The back story on the drawing that dominated the middle month of my summer bookzoompa.wordpress.com/2025/08/07/g...

So many shapes and lines interwoven and waiting, beckoning, taunting me with their symmetry, boldness, and restraint, to do more with them, which I finally did.

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Paula Beardell Krieg @paulakrieg.bsky.social · 06/08/2025

Recently took a class that deciphered the line work in an Alhambra tiling. I decided to color and weave it, too. Then went looking for a photo of the actual wall. Hard to find! Was so pleased to find a collection taken by @hpicciotto.bsky.social posted on www.mathed.page/symmetry/spa....

My hand drawn mage based on an Alhambra. repeat pattern . Within this ten inch square there are lines colored with red, chartreuse, turquoise, purple and a bit of gold and black. The systems of interlocking and woven paths are kind of mind boggling and seems to have worked their way into my soul .

A close up of my drawing of the Alhambra tiling. Even in this small area there are dozens of under and oven weaving of lines. There are many shapes that are locked together.

A photo of The tiling at the Alhambra, taken by Henri Picciotto

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Paula Beardell Krieg @paulakrieg.bsky.social · 20/04/2025

A sweet origami basket for fidgety fingers on Easter morning. wp.me/pEFoL-3Jt

A shy little plastic toy peeking out of the miniature origami basket she has claimed as her own. The basket is made from a 6 inch square, is decorated with delicate pink flowers on a green background, and seems very pleased to be the container for such an adorable toy

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Paula Beardell Krieg @paulakrieg.bsky.social · 21/03/2025

It's always a good day when I have something to share on Bluesky. I'm designing solids to use with third graders who are have shapes and magnets coming up in their curriculum. Am designing nets that play well with a punch out pattern block shapes. Irregular and regular hexagon and pentagons +

a regular hexagonal prism, an irregular hexagonal prism. and a triangular prism, all made with black paper. There are designs on the faces of the prisms that illuminate the decomposition of the larger shape. The pieces stay together by matching up magnetized surfaces.

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Paula Beardell Krieg @paulakrieg.bsky.social · 04/03/2025

I love that today's #MathArtMarch is Swirly. Here's one of my hand marbled papers, which shows a super tricky design , dubbed the Galen after creator Galen Berry. I think that it could be classified as a glide reflection design. Certainly not perfect but it's got the structure? thoughts?

Marbled paper, called the Galen design after Galen Berry who figured out some super tricky moves to make this.

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Paula Beardell Krieg @paulakrieg.bsky.social · 04/03/2025

So pleased to be part of seattlemathmuseum.org/intersections Mathematics and Art Intersections show! Scroll down through the link above to see lots of awesome work by many people.

Geometric shapes on a desk. Compound of two cubes and its convex hull.

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Paula Beardell Krieg @paulakrieg.bsky.social · 04/03/2025

Wasn’t sure what do post for day 3 of #MathArtChallenge #MathArtMarch -Nature- until I saw @baabbbaash.bsky.social day 1 post. Perfect inspiration.

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