a) Create a three-dimensional coordinate system as a diagonal image.
b) Draw the three points (A,B,C) in the coordinate system.

c) Calculate all lengths and angles of the triangle (A,B,C). → Calculate all angles with both the cosine set and also the scalar product. In the end s um up all the angles to get 180
d) Calculate the coordinates of the straight middles (middle of AB, AC, BC).
e) Set for all straights, which go from one angle to the opposite one, a parameter representation
f) Calculate the intersection of two straights and draw them in your coordinate system. Use the point probe with the other two straights. Prove that this is the main emphasis of the triangle.
g) Calculate under which angle the three degrees are cutting each other. The sum of all cutting angles must be 360.
h) Use the fourth point (D) to make a tetrahedral. Draw it in ur coordinate system.
I) Calculate the three remaining edge lengths of the tetrahedral and at least one of the three other triangles with its straight middle. Make the probe for the angle summation. Calculate the main emphasis of the new triangles in which their corner is the main emphasis of A,B,C.
j) Set up all four straights which go from one corner point of the tetrahedral to the main emphasis of the opposite traingle. Formulate them in the parameter representation. Calculate the intersection from two of such straights. Do the point probe with the other two straights. Profe that this is the main emphasis of the tetrahedral.
k) Calculate in which relationship the main emphasis of the tetrahedral divides the four straights from their corners to the straight middles.
l) Formulate the parameter form of the flats (A/B/C, A/B/Main emphasis, B/C/Main emphasis, A/C/Main emphasis). Define the normal forms for each flat.
m) Calculate the distance between the corner points of the tetrahedral to the opposite flat. For your calculations use the parameter representation and the normal form.
n) Calculate the flat area of all four triangles and the volume of the tetrahedral. Use the volume formula from a pyramid for at least two triangle areas and their appropriate heights. So at first calculate the four heights of the tetrahedral (it means the distances from the corners to the opposite triangle areas)
o) Calculate the angles of the triangle areas which form the xy-flat
p) Set up the perpendicular planes for all six sites.
q) Use a equating process for three of these flats (task p) and calculate the intersection of these three. Use the point probe with the other three flats.
r) Calculate the distance between all four corners from the intersection of task q. All distances must be the same length