Platonic Solids have been studied for thousands of years for its mathematical beauty and symmetry. The five platonic solids are:

Read below to plot the same on an excel graph and view by rotating about the axis

First let us consider say Octahedron of unit edge length

The vertices of the regular octahedron with its centre at origin will be as below. let us enter these in excel worksheet as Dynamic tables

Alt_coordinates-of-octahedron.jpg

click on the any cell in the table created and go to design tab and enter the table name -in this case as Octahedroncoordinates

Capture

Below this Create another Dynamic table with same table headings and enter the formulae as shown in the below images in all three column cells

octahedron_Vertices_xyz coordinates_platonic solid x

octahedron_Vertices_xyz coordinates_platonic solid y

octahedron_Vertices_xyz coordinates_platonic solid z

Enter  the vertice names in such order that it all the edges are connected. the x y and z co ordinate values appear automatically.

order

Select the x and y co ordinate columns in the table and insert a scattered chart

2D graph plot x and y.png

Only the x-y co ordinates are plotted & z  dimension is not visible when seen from x-y plane unless the object is rotated about y axis and x axis.

To rotate about the axes we  need to make use of transformation matrices

About X axis Transformation matrixAbout Y axis Transformation matrix.jpgAbout Z axis Transformation matrix

To obtain one resultant of all the three matrices first multitpy(matrix mautiplication)

[Z] * [X]; then multiply the product with the [Y] matrix

ie., [[Z] * [X]] * [Y] = R =Resultant Matrix

 Create the final dynamic table with SUMPRODUCT formula as below:

sumproductsumproduct1sumproduct3

Now drag the Table so that table size becomes equal to previous table’s size.

GRAPH SCATTERED.jpg

To rotate the solid we need to change the angle on which the transformation matrix is dependant, let us make it say 30 degree about z axis, 30 Deg about X axis and 5 Degree about Y axisRotate about axes

The graph changes to

Rotated Octahedron.jpg

you can change the angles as you like depending on the view you want to see.

Similarly rest of the Platonic solids can be represented

Thank you.

Please click here to the download the excel file.

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