Finalist

Triskelion Blocks
Akihiro Matsuura, Hiroshi Shirane

Akihiro Matsuura, Hiroshi Shirane “Triskelion Blocks” 2017, Material: VeroCyan,VeroMagenta,VeroYellow, Size: 75W x 60D x 9H (mm)A triskelion is an iconographic pattern that consists of three legs (or spirals) having three-fold rotational symmetry. We make use ofthis strange but intriguing figure as a motif of our new construction toy. We present two families of triskelion blocks with/without acentral equilateral triangle, where one block is connected to another at its concave parts in three directions. Such connection withsome tiling properties can be effectively used in constructing various shapes using the blocks. One can also enjoy “balancing play” ofphysically standing constructed shapes on the ground which reminds us of coordinated group gymnastics.

34

Finalist

Keywords: triskelion, construction toy, rotational symmetry

1 Basic Ideas & Figures

We make use of this strange but fascinating figure of three

A triskelion or triskele is a classical iconographic pattern thatlegs as motif for our new construction toy. Two basic planeconsists of three spirals placed with three-fold rotational

figures we use are shown in Figure 2 (let us call them figures

symmetry. It is frequently used with a representation of three

T1 and T2). Both figures have three legs with distinct (RGB)

bent human legs, which are seen for example in the flags ofcolors, where the left one has no center triangle but the right

Sicily and the Isle of Man [1] shown in Figure 1.

one has, i.e., the yellow equilateral triangle.

Figure 1: The flag of the Isle of Man

Figure 2: Two triskelion-like figures T1 and T2.

35

Finalist

Figure 6: The family of figures for T1 (leg length = 1, 2, 3).

Figure 3: Connections of T1’s or T2’s and the gymnastic pose.

Figure 7: The family of figures for T2 (leg length = 1, 2, 3).
Figure 4: Circular connection of T1’s and T2’s.

Figure 8: Circular connections for T1-family (leg length = 1,3).

Figure 5: The slilding property of T1 and T2.

The common property of these figures desirable for a con-physically-balanced two persons, which will make the playstruction toy is that a leg can be connected to the concave

more entertaining and imaginative. Furthermore, thesepart between two legs of another piece as shown in Figure 3,

triskelion-like figures have some beautiful geometricleft. This makes the figures to connect in three directions andproperties on tiling. Namely, six T1’s and six T2’s can behelps to create a variety of shapes. We also emphasize thatconnected in a circular way as shown in Figure 4 and these

the connected figures are just like the gymnastic pose ofconnections are extended infinitely in a recursive way. Espe-36

Finalist

Figure 9: Circular connections for T2-family (leg length = 1,3).

cially on T1, the central black part is again the shape of T1
and T1’s radially tile the whole plane.
The final typical property of T1 and T2 that we figured out
after prototyping and playing around with the pieces is that

Figure 10: Some constructions.

when we try to disconnect the three pieces from theinterlocking situation in Figure 5, left, we can succeed it byjust sliding two of the pieces, say, green and blue ones sincethen the remaining red piece slides out rather automaticallyvertically and construction can be 3-dimensional. All thewithout direct manipulation.

models were designed using the 3D CAD system 123D

Now, we show families of triskelion figures for T1 and T2 that

Design of Autodesk and output in the STL format. The six

preserve the properties of leg connection and recursive tiling.

models are shown in Page 1.

First, we illustrate the family for T1 with leg length 1, 2, and3 in Figure 6 and the family for T2 in Figure 7. (The figures

3 Prototyping & Some Constructionsof leg length 1 are rather exceptional but since they also have

We made prototypes of the blocks using PLA resin and thethe required geometric condition, here we include them).

3D printer Replicator 2. Here we show some of theconstructions using the prototypes in Figure 10.

2 Software & System

The circular connections for the figures in Figures 6 and 7

3D models were made by adding a constant depth to theare shown in Figures 8 and 9, respectively.

figures in Section 1. When the length of unit triangle is 1,
the depth is set to be half of 3 squared, i.e., 0.86 (roundedReferencesoff) since then the depth parts can be inserted to blocks[1] Triskelion, http://en.wikipedia.org/wiki/Triskelion

37