Paula Beardell Krieg
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paulakrieg.bsky.social
Paula Beardell Krieg
@paulakrieg.bsky.social
180 followers 100 following 160 posts
Happy to share art and math play
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paulakrieg.bsky.social
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.
Folding a polyhedron Using paper pedestal for an octahedron Wooden sculpture on paper. PO edestal
January 28, 2026 at 5:02 PM
paulakrieg.bsky.social
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.
paulakrieg.bsky.social Paula Beardell Krieg @paulakrieg.bsky.social · 17d
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...
January 27, 2026 at 5:31 PM
paulakrieg.bsky.social
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...
January 26, 2026 at 9:21 PM
paulakrieg.bsky.social
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.
January 25, 2026 at 12:47 AM
paulakrieg.bsky.social
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
January 22, 2026 at 3:15 PM
paulakrieg.bsky.social
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, waiting to be opened Cube, nicely splayed to reveal an octahedron whose vertices are the mid points of the faces of the cube.
January 18, 2026 at 6:27 PM
paulakrieg.bsky.social
Using pattern blocks motifs on larger pattern block shapes, in different arrangements. #patternblocks #symmetry #paperconstructions
#triangles +
Triangles strewn about Simple rational symmetry of triangles Refection of a triangle, which,together , glide
January 13, 2026 at 4:07 PM
paulakrieg.bsky.social
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.
A stack of blocks with designs. Blocks with a single design reproduced on all faces.
January 9, 2026 at 3:26 PM
paulakrieg.bsky.social
Snowy day here in upstate NY. Leaning into it.
#snowflakeSymmetry
Coloful six sided snowflakes, to brighten your day.
January 7, 2026 at 8:57 PM
paulakrieg.bsky.social
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. Scrolls escaping from their box.
January 2, 2026 at 4:23 PM
paulakrieg.bsky.social
To my friends on Bluesky, best wishes for the new year.

#geometry
#star
#eightpointedstar
#IGP
Eight-pointed star created with Islamic Geometry during a class hosted by Global Centre of Islamic Art. Blues, greens, and purples surround a fiery colored star.
January 1, 2026 at 10:27 PM
paulakrieg.bsky.social
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
December 30, 2025 at 9:14 PM
paulakrieg.bsky.social
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.
December 30, 2025 at 9:05 PM
paulakrieg.bsky.social
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...
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…
bookzoompa.wordpress.com
December 29, 2025 at 10:45 PM
paulakrieg.bsky.social
A pattern block reflection to brighten your day.
#mtbos
#geometry
#patternblocks
#reflection
2 hexagons and a rhombus, all dressed up in colorful shapes, with a hexagonal reflection below.
December 9, 2025 at 6:14 PM
paulakrieg.bsky.social
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
November 19, 2025 at 3:46 PM
paulakrieg.bsky.social
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.
November 19, 2025 at 3:38 PM
paulakrieg.bsky.social
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.
November 17, 2025 at 6:31 PM
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
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