# GMTRCPLY - GeoMeTRiCPLaY

## GeoBender Upsizing Projects

Double-Sizing
Special Upsizing

 Introduction to Double-Sizing: Base Combos and Source Shapes

### Introduction to Double-Sizing

Upsizing is a common challenge with 2D- and 3D-tilings. This can be done with ShaShiBo and GeoBender as well. For double-sizing a single shape, you need eight units. But it can be helpful to have a ninth as "live" model.

There are two important combinations of two when it comes to double-sizing:
[a] Top-Left: UFO (No.9) + Cube (No.1) = Diamond
[b] Top-Right: UFO (No.9) + Ring (No.8) = Seashell

If you take any four of these (4+0, 3+1, 2+2), you can easily build double-size versions of eight shapes by simply connecting these base combos. The eight target shapes are, from top-middle-left, counter-clockwise to top-middle-right:
[1] No.01: Cube
[2] No.21: Chair, Open Cube
[3] No.32: Mouse, Owl
[4] No.06: Hive, Stacked Cubes
[5] No.09: UFO
[6] No.71: Cube Eater
[7] No.59: Snail, Open Sphere
[8] No.10: Sphere, Cocoon

### The Buzzer

This is a shape that I wanted to double-size for a long time, in the meantime I finished it.

For the first build I started with two sub-shapes I identified, and I knew how to double-size. So I only had to deal with the other half. The first try was a bit unstable, so I modified it to get two units tangled to make it more stable.

Then I remembered that the "Buzzer" can be opened to make shape number 41. But my double-size shape could only be divided the other way, but not the required way. So I decided to start from scratch with the split in mind.

The first attempt of the second build had a spot where two shapes touched, but without magnets. With some modifications, I managed to get a build where the two shapes were tangled and with magnetic hold.

The final version can be split in half both ways, which means that it can actually be split up in four segments.

Please note that there is no hinge as in the original single-size "Buzzer". The scond image shows the segments attached to make a double-size number 41. Both, GeoBender and ShaShiBo Shape Guides show the shape upside down.

### The Opened Buzzer

See above for explanations.

### Thomas' Box (TomBox)

A TomBox is a combination of two units. Based on the appearance, a TomBox is self-multiplying, you just have to combine n×n×n together.

However, a TomBox can be flipped open at six positions: Four large pyramids at four of the corners, and two small parts.

It is possible to build a double-size TomBox that supports the four large flips at double-size. The two small flips can't be modeled in double-size. But if you are fussy, you can build the double-size TomBox in such a way that a single-size small flip is possible at all of the eight corners.

### Floating Cubes, Tetracubes

I call this combo "Floating Cubes", because it seems that they are not connected. Actually, they share six edges.

The base shape is made from four UFO shapes. The double-sized shape looks very impressive, but is actually one of the easy double-sizing jobs. The central element is simply made from four "Seashell" combos, the four Cube ends connected to the central element are mande from three "Diamond" combos each.

 Large Octahedron

### Large Octahedron

The "atomic" Octahedron is equal to four elements.

What you see here is an Octahedron of 4× the size. Having 4× in 3D means 4×4×4 as many elements. That would be a total of 256 elements, equal to 21 1/3 Units. When using 21 Units, some empty space equal to 4 elements is hidden inside.

The photo shows the transition from a Torus to the Octahedron by adding a smaller Octahedron at the top and the bottom of the Torus.

 Large Rhombic Pyramids - Left: Bottom/Side View, Right: Top View

### Large Rhombic Pyramid

The "atomic" Rhombic Pyramid is equal to two elements put together at their "outside" faces.

What you see here are Pyramids of 4× the size. Having 4× in 3D means 4×4×4 as many elements. That would be a total of 128 elements, equal to 10 2/3 Units. When using 10 Units, some empty space equal to 8 elements is hidden inside.

The best part about having mastered the Large Pyramid is the fact that two of these can be combined at their Rhombic faces to make a Large Octahedron.

The  Large Octahedron  was built using 21 Units. Compared to two Large Rhomnic Pyramids, that's one Unit more. When having a total of 2×8 = 16 elements of empty space, you can use one more unit to make the object more solid. Then there is only empty space equal to 4 elements left.

Hans-Jürgen Reggel   ·   http://www.hjreggel.net/gmtrcply/   ·   Imprint   ·   2023-10-05 ~ 2023-10-21