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Modular Origami — Balls and Polyhedra

Models folded and photographed by Michał Kosmulski. Modules designed by their respective authors.
Click on images to enlarge them. Links in image titles lead to pages with more information about each particular object.

Cube - trapezoid egde module (TEM)

Cube

Made from Michał Kosmulski's TEM (Trapezoid Egde Module) (12 modules).

Hexagonal prism - trapezoid egde module (TEM)

Hexagonal prism

Made from Michał Kosmulski's TEM (Trapezoid Egde Module) (18 modules).

Icosidodecahedron - jitterbug module

Icosidodecahedron

Made from Tung Ken Lam's jitterbug module (20 modules).

Cube - oxi module

Cube

Made from Michał Kosmulski's Oxi module (24 modules).

Truncated cube - PHiZZ module

Truncated cube

Made from Thomas Hull's PHiZZ unit (24 modules).
Generally, PHiZZ units are always connected in such way that three modules meet at each vertex. However, one can connect just two modules at some points, thus making the edges longer and making it possible to create faces of shapes which are not possible with "regular" PHiZZ connections (for example octagons).

Icosahedron - 120 degree module

Icosahedron

Made from Francis Ow's 120 degree module (30 modules, pointing inwards).

Icosahedron - 120 degree module

Icosahedron

Made from Francis Ow's 120 degree module (30 modules, pointing outwards).

Icosahedron - penultimate module

Icosahedron

Made from a modified version of Robert Neale's penultimate module (30 modules, pointing outwards).

Icosahedron - sonobe units pointing inside

Icosahedron

Made from Sonobe module (30 modules, pointing inwards).

Umbrella dodecahedron

Umbrella Dodecahedron

Made from M. Mukhopadhyay's umbrella dodecahedron module (30 modules).

Poinsettia ball and real flower

Poinsettia ball

Model is placed near a real Poinsettia flower for comparison.

Made from M. Mukhopadhyay's poinsettia ball module (30 modules).

Icosahedron - 60 degree module

Icosahedron

Made from Francis Ow's 60 degree module (scroll down the linked page for unit folding instructions) (30 modules).

Icosahedron - modified 60 degree module

Icosahedron

Made from a modified version of Francis Ow's 60 degree module (scroll down the linked page for original unit folding instructions) (30 modules).

Dodecahedron - modified 60 degree module

Dodecahedron

Made from a modified version of Francis Ow's 60 degree module (scroll down the linked page for original unit folding instructions) (30 modules).

Dodecahedron - TEM

Dodecahedron

Made from Michał Kosmulski's TEM (Trapezoid Egde Module), antisymmetric variant (30 modules, "inverted" vertices).

Truncated octahedron - TEM

Truncated octahedron

Made from Michał Kosmulski's TEM (Trapezoid Egde Module), antisymmetric variant (36 modules).

Truncated octahedron - penultimate module

Truncated octahedron

Made from Robert Neale's penultimate module (36 modules).

Truncated octahedron - modified 60 degree module

Truncated octahedron with inverted spikes on all faces

Made from a modified version of Francis Ow's 60 degree module (scroll down the linked page for original unit folding instructions) (36 modules). Note that in this modification, the angle at the module's tip is NOT 60 degrees.
[ 3D image ]

Truncated cube - super simple isosceles triangle module

Truncated cube with inverted spikes on all faces

Made from M. Mukhopadhyay's super simple isosceles triangle module (module also attributed to Jeannine Mosely and Roberto Morassi) (36 modules).

Tetrahedron, cube and two octahedra - Sturdy Edge Module

Tetrahedron, cube and two octahedron variants

Made from Michał Kosmulski's Sturdy Edge Module (StEM) (6 + 12 + 2 * 12 = 42 modules).

These very simple assemblies show basic usage of the StEM unit. Note how the tetrahedron looks almost like a cube due to the module's large breadth. The two octahedra demonstrate how triangular faces can be folded with module edges pointing outwards or inwards.

Truncated tetrahedron - 60 degree module

Truncated tetrahedron

Made from Francis Ow's 60 degree module (scroll down the linked page for unit folding instructions) (42 modules).

Truncated tetrahedron - Simple Edge Unit

Truncated tetrahedron

Made from Michał Kosmulski's Simple Edge Unit (SEU) (42 modules).

Truncated tetrahedron - Sturdy Edge Module

Truncated tetrahedron

Made from Michał Kosmulski's Sturdy Edge Module (StEM) (42 modules).

Rhombicuboctahedron - penultimate module

Rhombicuboctahedron

Made from Robert Neale's penultimate module (48 modules).

Rhombicuboctahedron - Simple Edge Unit

Rhombicuboctahedron

Made from Michał Kosmulski's Simple Edge Unit (SEU) (48 modules).

Rhombicuboctahedron - Sturdy Edge Module

Rhombicuboctahedron

Made from Michał Kosmulski's Sturdy Edge Module (StEM) (48 modules).

Tetrahedra, cubes and octahedra - comparision of Simple Edge Unit made of 2:1 and square paper

Tetrahedra, cubes and octahedra — comparison of two SEU unit variants

Made from Michał Kosmulski's Simple Edge Unit (SEU) 2 * (6 + 12 + 12) = 60 modules.

These very simple assemblies show basic usage of the SEU unit. Two variants are shown: the standard, elongated module made from 2:1 paper and the Sonobe-like variant made from square paper. Note how the tetrahedron made from Sonobe-like variant becomes a cube due to the pyramids formed by modules' sides aligning.

Truncated cuboctahedron - super simple isosceles triangle module

Truncated cuboctahedron with inverted spikes on all faces

Made from M. Mukhopadhyay's super simple isosceles triangle module (module also attributed to Jeannine Mosely and Roberto Morassi) (72 modules).

Truncated octahedron - oxi module

Truncated octahedron

Made from Michał Kosmulski's Oxi module (72 modules).

Truncated tetrahedra - comparison of Simple Edge Unit and Sturdy Edge Module

Two truncated tetrahedra — comparison of SEU and StEM units

Made from Michał Kosmulski's Simple Edge Unit (SEU) (42 modules) — left piece, and Michał Kosmulski's Sturdy Edge Module (StEM) (42 modules) — right piece, 84 modules altogether.

Notice how the two units are similar in appearance but their different widths affect the whole model's look. SEU made from 2:1 aspect ratio paper was used for the left model. SEU units are narrower so more of the model's inside is visible, but on the other hand StEM's greater breadth allows for more precise connections. With high-tension angles found in this model, SEU units tend to bend and deform much more than StEM, as can be seen close-up.

Truncated octahedron - Open Frame I unit (bow-tie variant)

Truncated octahedron

Made from Tomoko Fuse's Open Frame I unit (bow-tie motif) (84 modules).

Decorated dodecahedron - penultimate module

Decorated dodecahedron

Made from a modified version of Robert Neale's penultimate module (90 modules, pointing outwards, 5-triangle groups depressed to point inwards).

Dodecahedron with pentagonal pyramids on all faces and inverted spikes on pyramids' side faces - trimodule

Dodecahedron with pentagonal pyramids on all faces and inverted spikes on pyramids' side faces

Made from Nick Robinson's trimodule (90 modules).

Fullerene (truncated icosahedron) - penultimate module

Fullerene (truncated icosahedron)

Made from Robert Neale's penultimate module (90 modules).

Buckyball (90 edges) - PHiZZ variant 1

Buckyball (90 edges)

Made from a variant of Thomas Hull's PHiZZ unit (90 modules).
[ 3D image ]

Buckyball (90 edges) - PHiZZ variant 2

Buckyball (90 edges)

Made from a variant of Thomas Hull's PHiZZ unit (90 modules).

Rhombicuboctahedra - comparison of Simple Edge Unit and Sturdy Edge Module

Two rhombicuboctahedra — comparison of SEU and StEM units

Made from Michał Kosmulski's Simple Edge Unit (SEU) (48 modules) — left piece, and Michał Kosmulski's Sturdy Edge Module (StEM) (48 modules) — right piece, 96 modules altogether.

Notice how the two units are similar in appearance but their different widths affect the whole model's look. SEU made from 2:1 aspect ratio paper was used for the left model. StEM's larger flaps allow for more precise connections as can be seen near the vertices in close-up.

Buckyball (120 edges) - PHiZZ module

Buckyball (120 edges)

Made from Thomas Hull's PHiZZ unit (120 modules).

Modified buckyball (120 edges) - PHiZZ unit and penultimate module

Modified buckyball (120 edges)

Made from 120 units altogether: Thomas Hull's PHiZZ unit (60 modules) and Robert Neale's penultimate module (60 modules).
This is my experiment in modular origami made from two different types of units. PHiZZ and penultimate modules are quite similar, so I decided to try using both in a single model. The result is a buckyball whose pentagonal faces protrude a little from the ball's main body, giving it a very distinct "organic" look. This shape can be considered an intermediate between the 120-edge buckyball and the dodecahedron with prisms on all faces.

Decorated rhombicuboctahedron - penultimate module

Decorated rhombicuboctahedron

Made from Robert Neale's penultimate module (120 modules).
[ 3D image ]

Dodecahedron with prisms on all faces - penultimate module

Dodecahedron with prisms on all faces

Made from Robert Neale's penultimate module (150 modules).

Buckyball (210 edges) - PHiZZ variant 3

Buckyball (210 edges)

Made from a variant of Thomas Hull's PHiZZ unit (210 modules).
[ 3D image ]

Buckyball (210 edges) inside view - PHiZZ variant 3
Golden ball (snub dodecahedron) - penultimate module

Golden Ball (snub dodecahedron)

Made from a modified version of Robert Neale's penultimate module (210 modules, pointing outwards).

Octahedral lattice - penultimate module

Octahedral lattice

Made from Robert Neale's penultimate module (240 modules).

Large icosahedron - sonobe module

Large icosahedron (=truncated icosahedron with pyramids on all faces)

Made from Sonobe module (270 modules).
This icosahedron has 9 triangular pyramids pointing inwards on each face. The same shape can also be described as a truncated icosahedron whose each face has been replaced with a pentagonal or hexagonal pyramid bearing a triangular pyramid on each face. The three images show this solid from the top, from the bottom and from the side, respectively.

Large icosahedron - sonobe module
Large icosahedron - sonobe module
Buckyball (truncated icosahedron) - open frame II (plain) module

Truncated icosahedron with tessellated hexagonal faces and inverted pyramids on pentagonal faces

Made from Tomoko Fuse's Open Frame II unit (plain) (270 modules).

Buckyball (truncated icosahedron) - open frame II (plain) module
Decorated icosidodecahedron - penultimate module

Decorated icosidodecahedron

Made from Robert Neale's penultimate module (360 modules).
One of the larger models I have designed, this icosidodecahedron has pentagonal faces made up of small triangular pyramids and triangular faces replaced with cubes which form the "decoration".

Decorated icosidodecahedron - penultimate module
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