Paula Beardell Krieg
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paulakrieg.bsky.social
Paula Beardell Krieg
@paulakrieg.bsky.social
160 followers 95 following 120 posts
Happy to share art and math play
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paulakrieg.bsky.social
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
November 15, 2025 at 2:34 AM
paulakrieg.bsky.social
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.
November 11, 2025 at 1:58 AM
paulakrieg.bsky.social
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.
October 19, 2025 at 9:18 PM
paulakrieg.bsky.social
We had our first brush with an autumn frost just last night. Suspecting it would be so, I took some photos of some end of season blooms. Glad to have these.
Shameless pink zinnia Perfect in pink cosmos
September 22, 2025 at 12:22 AM
paulakrieg.bsky.social
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.
September 1, 2025 at 3:35 AM
paulakrieg.bsky.social
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. Black box with cubes tucked in. 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.
August 31, 2025 at 1:59 AM
paulakrieg.bsky.social
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.
August 25, 2025 at 4:22 PM
paulakrieg.bsky.social
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.
August 24, 2025 at 12:48 AM
paulakrieg.bsky.social
So many people sent me yesterday’s NYT article on blossom fold that I couldn’t resist making one. Very pretty in three dimensions
August 21, 2025 at 11:28 AM
paulakrieg.bsky.social
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.
August 8, 2025 at 3:16 AM
paulakrieg.bsky.social
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
August 6, 2025 at 6:26 PM
paulakrieg.bsky.social
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
April 20, 2025 at 12:47 AM
paulakrieg.bsky.social
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. a net of a hexagon
March 21, 2025 at 1:52 AM
paulakrieg.bsky.social
Thank goodness for search engines. Found two Eulers. One in Queensland Australia, the other in Churchville NY.
Euler Road sign in Churchville NY, with a cornfield in the background Euler Street sign in Queensland Australia in a residential area.
March 11, 2025 at 5:06 PM
paulakrieg.bsky.social
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.
March 4, 2025 at 11:00 PM
paulakrieg.bsky.social
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.
March 4, 2025 at 10:35 PM
paulakrieg.bsky.social
not on my blog, but in my class sites. Am happy to share with you anything you'd like, but you'd have to meet with me so that I could explain a few things. Here's a photo of the cube that goes inside, the expanded RD, and a specially made 12 sided box to put them in.
Geometric shapes that nest together. A cube, a rhombic dodecahedron, and a 12 sided box
March 4, 2025 at 9:54 PM
paulakrieg.bsky.social
Wasn’t sure what do post for day 3 of #MathArtChallenge #MathArtMarch -Nature- until I saw @baabbbaash.bsky.social day 1 post. Perfect inspiration.
March 4, 2025 at 1:52 AM
paulakrieg.bsky.social
#MathArtMarch day 2: On a square grid
March 2, 2025 at 9:49 PM
paulakrieg.bsky.social
I generally shy away from daily prompts. However I find @ayliean.bsky.social pretty irresistible. Hence #MathArtMarch Day 1 Circles. This is a bubble print , where you can see the 120 degree angles that form where three bubbles meet.
Colorful bubble print
March 2, 2025 at 9:46 PM
paulakrieg.bsky.social
Once again having a difficult time preparing for the class I'm teaching later today about #cubes. The rabbit holes I stumble into are irresistible. Last week we made a #rhombicdodecahedron which unfurled into cube & revealed an inner cube. Today I designed a box to hold it.Not in our syllabus.
Box for and units of a rhombic Dodecahedron. An closed and an open box for the rhombic dodecahedron
February 25, 2025 at 7:09 PM
paulakrieg.bsky.social
Prepping for tonight's zoom class, having an awful time of it because I keep wanting to play around with the #cubes I'll be teaching rather than doing any actual prep.

#CenterForBookArtsNYC
#SecretLivesOfCubes
Stack of cubes
February 18, 2025 at 8:43 PM
paulakrieg.bsky.social
I've been waiting for you to taunt me. Here are my outside and inside photos.
Snow outside Bloms indoors
February 12, 2025 at 4:09 PM
paulakrieg.bsky.social
Last night had the best time working with adults, pouring ourselves into #cubes. One part was about the tension between hexagons and squares and how they make peace with each other in the diagonal slice of a #cube. Faces just lit up with delight when the hexagon revealed itself with the cube.
Net of the diagonal halves of a cube, with magnets and paperclips ready to be embedded within. Diagonal halves of a cube, revealing hexagonal face
February 12, 2025 at 3:19 PM
paulakrieg.bsky.social
Whoa! Look what Gathering 4 Gardner is presenting tomorrow, Tuesday Jan 21. The timing of this is difficult for me but will do all I can to be try to be there. This is exactly the sort of things I've been thinking about, albeit in simpler terms. www.gathering4gardner.org/com-2025-01-...
announcement for a Garthering 4 Gardner event, featuring a dodecahedron
January 20, 2025 at 3:21 PM