**2. Hypercube models**

*Truss and Frames - Recent Advances and New Perspectives*

Hypercube originates from a point, which is a hypercube of dimension zero [5, 6]. If the point moves to another point, it makes a line, which is a unit hypercube of dimension one. If the line moves out in a perpendicular direction, it makes a square, which is a unit hypercube of dimension two. If the square moves to a perpendicular direction, it makes a cube, which is a unit hypercube of dimension three. And if the cube moves to the fourth dimension, it is called a four-dimensional hypercube as a unit tesseract.

In the engineering material field, one of the simplest lightweight truss model is truss cubic, which is defined by Gibson and Ashby [7]; it is a model of hexagonal truss to define an ideal solution for honeycomb, open cell, or closed cell model. This is based on the three-dimensional stereoscopic structure. It can create a model which is hypercube truss model composed of a hexagonal truss inside and a hexagonal truss inside. Thus, this paper is focused on studying the hypercube concept to

If tesseract is composed of two regular hexahedrons, i.e., one is for outer structure and the other is for inner structure, with or without diagonal truss, then two types of model can be defined such as the core-filled or the core-spaced shape. That is, it depends with or without a truss in a diagonal direction. Therefore, this paper is

According to the reported papers on the mechanical properties of structures that

Three-dimensional printing skill is not a magic to create anything; it requires techniques to be used with materials. The most important is what the application is. Thus, depending on the skills of the materials, the quality of a product is decided. Recently, 3D printing skill is announced as a revolution in manufacturing technique and it has been developed more and more. From the beginning of the skill, it is defined various techniques like fused deposition modeling (FDM) [8, 10], selective laser sintering (SLS) [9], direct light processing (DLP) [7, 8, 12], stereolithography (SLA) [11, 13], laminated object manufacturing (LOM) [11, 14], stereolithography (SL) [14], mask projection stereolithography (MPSL) [14], three-dimensional printing (3DP) [14], droplet

are 3D printed with powders recently, there are advantages and disadvantages. The merits are to make a shape easily, to save time, to create a complex shape without any limited shape, and to make a high-quality part for the application in the aerospace or biomedical industry. Demerits are a high cost to create a product, a limited space to make a product, a limited materials such as metal powders, a required high quality equipment to produce high quality product, a need to hire a

make a unit model to apply for a sandwich core structure.

focused on studying two models defined as Type 1 and Type 2.

professional engineers to take control the equipment, etc.

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**Figure 1.**

*Schematic of a hypercube.*

For designed models, it is defined as an ideal mathematical solution. Based on the previous researchers, lattice or truss model defined as open cell model may have a correlation between relative elastic modulus as a function of relative density or between relative compressive yield strength as a function of relative density. Thus, **Figure 2** shows Type 1 and Type 2 shape. The next section shows details on stiffness or strength for both the models. Type 1 is core-filled model and Type 2 is a core-spaced model. Each model is created by the DMLS technique. And then both models are tested by compression. Before experimental testing for Type 1 and Type 2, they are checked for material properties of a specimen based on ASTM E8/E8M [25]. The specimen is made by DMLS and then tested by tension and compression to check the material properties.

**Figure 2.** *Samples made by the 3D printing DMLS skill: (1) is Type 1 and (2) is Type 2.*
