Represent 3D shapes in 2D with Excel scatter graph

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

TETRAHEDRON

OCTAHEDRON

CUBE

DODECAHEDRON

ICOSAHEDRON

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

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

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

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

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

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

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:

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

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 axis

The graph changes to

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.