## Introduction

This package is a curation made based on the poly package found on https://netlib.org/polyhedra/ (Original Help message), and the polyhedra database found on http://dmccooey.com/polyhedra/, both of which provide polyhedra databases on its own format. As such, Rpolyhedra provides with the following:

- A module to scrape the polyhedra for the different sources found with features for incremental correction of issues found and to be found in scraping process.
- A database of the scraped polyhedra.
- An R6 polyhedron representation with ‘rgl’ package visualizing capabilities.

## Usage

For final users, the package provides a common interface for accessing public polyhedra databases, analyze properties, compare and visualize them with RGL.

For advanced users, the package provides a simplified set of R6 objects to scrape and compare polyhedra databases.

### Get available polyhedra

Once the original files had been processed, a simple call to `getAvailablePolyhedra()`

retrieves a list of the available polyhedra with properties and status in the polyhedra database:

```
#show only the first 10 polyhedra.
head(getAvailablePolyhedra(), n = 10)
```

```
## source scraped.name symbol vertices faces
## 1 netlib tetrahedron {3,3}\t@Y sub 3 @ 4 4
## 31 netlib square pyramid (j1) \t@Y sub 4 @ 5 5
## 42 netlib triangular dipyramid (j12) \t@Y sub 3 @ 5 6
## 9 netlib triangular prism \t@P sub 3 @ 6 5
## 32 netlib pentagonal pyramid (j2) \t@Y sub 5 @ 6 6
## 3 netlib octahedron {3,4}\t@S sub 3 @ 6 8
## 37 netlib elongated triangular pyramid (j7) \t@Y sub 3 @ 7 7
## 74 netlib augmented triangular prism (j49) \t@Y sub 4 @ 7 8
## 43 netlib pentagonal dipyramid (j13) \t@Y sub 5 @ 7 10
## 2 netlib cube {4,3}\t@P sub 4 @ 8 6
## status
## 1 scraped
## 31 scraped
## 42 scraped
## 9 scraped
## 32 scraped
## 3 scraped
## 37 scraped
## 74 scraped
## 43 scraped
## 2 scraped
```

### Retrieve a polyhedron

The access to a particular polyhedron can be done with a call to `getPolyhedron(<<source>>, <<polyhedron.name>>)`

, which returns a Polyhedron object. For example, to retrieve a cube from the netlib database, the call would be:

`cube <- getPolyhedron(source = "netlib", polyhedron.name = "cube")`

## A demo

To try package functionality, a simple demo can be executed which shows the 5 regular polyhedra.

```
# 1. Obtain 5 regular solids
polyhedra.2.draw <- getAvailablePolyhedra(source = "netlib")
polyhedra.2.draw <- polyhedra.2.draw %>%
filter(scraped.name %in%
c("tetrahedron", "octahedron", "cube",
"icosahedron", "dodecahedron"))
# 2. Setup colors and scales
n <- nrow(polyhedra.2.draw)
polyhedron.colors <- rainbow(n)
polyhedron.scale <- 5
# 3. Open and setup RGL window
open3d()
```

```
## null
## 1
```

```
## Warning: 'rgl.bg' is deprecated.
## Use 'bg3d' instead.
## See help("Deprecated")
```

`rgl.viewpoint(theta = 0, phi=0, zoom=0.8, fov=1)`

```
## Warning: 'rgl.viewpoint' is deprecated.
## Use 'view3d' instead.
## See help("Deprecated")
```

```
# 4. For each polyhedron, setup rotation, position and render
for (i in seq_len(n)) {
# Obtain polyhedron
polyhedron.row <- polyhedra.2.draw[i,]
polyhedron.name <- polyhedron.row$scraped.name
polyhedron <- getPolyhedron(source = polyhedron.row$source, polyhedron.name)
# Setup angles, position into transformationMatrix
current.angle <- i/n * 2 * pi
tm <- rotationMatrix(current.angle, 1, 0, 0)
x.pos <- round(polyhedron.scale * sin(current.angle), 2)
y.pos <- round(polyhedron.scale * cos(current.angle), 2)
tm <- tm %*% translationMatrix(x.pos, y.pos, 0)
# Render
print(paste("Drawing ", polyhedron.name, " rotated ", round(current.angle, 2),
" in (1,0,0) axis. Translated to (", x.pos, ",", y.pos, ",0)",
" with color ", polyhedron.colors[i], sep = ""))
shape.rgl <- polyhedron$getRGLModel(transformation.matrix = tm)
shade3d(shape.rgl, color = polyhedron.colors[i])
}
```

```
## [1] "Drawing tetrahedron rotated 1.26 in (1,0,0) axis. Translated to (4.76,1.55,0) with color #FF0000"
## [1] "Drawing octahedron rotated 2.51 in (1,0,0) axis. Translated to (2.94,-4.05,0) with color #CCFF00"
## [1] "Drawing cube rotated 3.77 in (1,0,0) axis. Translated to (-2.94,-4.05,0) with color #00FF66"
## [1] "Drawing icosahedron rotated 5.03 in (1,0,0) axis. Translated to (-4.76,1.55,0) with color #0066FF"
## [1] "Drawing dodecahedron rotated 6.28 in (1,0,0) axis. Translated to (0,5,0) with color #CC00FF"
```