Torus Flowers in a Dodecahedron Vase
Cut Files
The .Studio file is for the Silhouette machine and the SVG file for the Cricut machine.
Here is the PDF to see how this project was created.
Here is the .Studio file.
Here is the SVG. The file extends beyond the viewable area. Zoom out to see the entire file.
Designing the Flowers in TurtleStitch
I began with a flower created using a custom Petal Block in TurtleStitch. https://www.turtlestitch.org/users/Elaine/projects/Petal%20Flower The design combines arcs and rotations to form a symmetrical flower pattern. Once complete, I exported the design as a DXF file.
I began with a flower created using a custom Petal Block in TurtleStitch. https://www.turtlestitch.org/users/Elaine/projects/Petal%20Flower The design combines arcs and rotations to form a symmetrical flower pattern. Once complete, I exported the design as a DXF file.
Modifying in Silhouette Studio - Please check out the PDF file included in this posting to see the photos of this process and the flower that was produced.
In Silhouette Studio, I refined the flower shape using the Offset menu:
First, I applied an internal offset of 0.075 inches to the entire flower. This created a delicate inner contour.
Then, I added an external offset of 0.075 inches to the outer line only, preserving the boundary shape while adding definition.
To create variation and depth, I enlarged the inner petals by 125% and removed the central circular piece, giving the flower a layered, airy appearance.
The result is a lacy, stylized flower perfect for papercrafting—and just the right size to fit in the openings of a dodecahedron vase. A dodecahedron is a Platonic solid made of 12 regular pentagons. In Silhouette Studio, I created a net, an unfolded layout that could be cut, folded, and assembled into the vase. On ten sides of the dodecahedron, I added windows of lacy flowers using Silhouette software, which were then backed with vellum.
In Silhouette Studio, I refined the flower shape using the Offset menu:
First, I applied an internal offset of 0.075 inches to the entire flower. This created a delicate inner contour.
Then, I added an external offset of 0.075 inches to the outer line only, preserving the boundary shape while adding definition.
To create variation and depth, I enlarged the inner petals by 125% and removed the central circular piece, giving the flower a layered, airy appearance.
The result is a lacy, stylized flower perfect for papercrafting—and just the right size to fit in the openings of a dodecahedron vase. A dodecahedron is a Platonic solid made of 12 regular pentagons. In Silhouette Studio, I created a net, an unfolded layout that could be cut, folded, and assembled into the vase. On ten sides of the dodecahedron, I added windows of lacy flowers using Silhouette software, which were then backed with vellum.
After cutting, I folded along each edge and carefully glued the structure into place.
The Torus as Floral Inspiration
The true inspiration for this flower design comes from the torus, a fascinating shape formed from a stack of Villarceau circles—thin, half-moon slices that curve and weave together to form a donut-like shape.
There are two types of Villarceau circles used in the construction, each with opposite slits that allow them to slide into one another. This assembly process creates not just a torus, but a dynamic, flexing form that can be transformed into petal-like structures when the slices are altered.
I’ve explored this concept in previous work by modifying the edges and angles of the Villarceau circles. From this exploration, four unique torus-inspired flowers emerged. Each flower preserves the essential tension and curvature of the torus but expresses it in a new, floral form.
The fifth flower in this collection is a reimagined torus, approximately half the size of the original. It features a modified Villarceau circle, and must be strung together at the bottom point to maintain alignment. Please note—this smaller torus requires significant patience to assemble. The last few slices must be carefully bent and stretched into place without tearing or creasing.
Want to try it yourself? Cut 16 slices to form one flower. There will be 8 slices of each type since the slices slide into one another. Here's a basic tutorial on weaving Villarceau circles, originally used for a honeycomb pumpkin. The principle is the same—just with a toroidal twist!
The true inspiration for this flower design comes from the torus, a fascinating shape formed from a stack of Villarceau circles—thin, half-moon slices that curve and weave together to form a donut-like shape.
There are two types of Villarceau circles used in the construction, each with opposite slits that allow them to slide into one another. This assembly process creates not just a torus, but a dynamic, flexing form that can be transformed into petal-like structures when the slices are altered.
I’ve explored this concept in previous work by modifying the edges and angles of the Villarceau circles. From this exploration, four unique torus-inspired flowers emerged. Each flower preserves the essential tension and curvature of the torus but expresses it in a new, floral form.
The fifth flower in this collection is a reimagined torus, approximately half the size of the original. It features a modified Villarceau circle, and must be strung together at the bottom point to maintain alignment. Please note—this smaller torus requires significant patience to assemble. The last few slices must be carefully bent and stretched into place without tearing or creasing.
Want to try it yourself? Cut 16 slices to form one flower. There will be 8 slices of each type since the slices slide into one another. Here's a basic tutorial on weaving Villarceau circles, originally used for a honeycomb pumpkin. The principle is the same—just with a toroidal twist!
The red flower torus (it looks like a half of a heart) is made with the technique in this blog posting. A thread is used to hold the torus together. https://papercraftetc.blogspot.com/2021/07/a-stem-project-amazing-slice-form.html
Assembly in the Dodecahedron Vase
The vase is made by gluing the vellum to the the sides of the dodecahedron. The dodecahedron is glued together to form the vase.
The stems are two ply. The buds are splayed outward and are not glued together.
The stems are folded in half and are glued to the base.
Bottom view of base. Two pentagons are glued to this bottom for support and then glued to the top of the dodecahedron vase.
The twelve flowers are glued to the tops of each stem. The vellum windows on each face allow the light to shine through and highlight the layered offset curves of the TurtleStitch created flowers. Each window becomes a frame for the toroidal geometry inside.
The combination of curved forms and sharp dodecahedral edges creates a striking contrast—one that’s both organic and mathematical.
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