ρ = 19 (slider from 6 to 20, step 0.1)
φ = 6.24827782 rad (slider from 0 to 6.283185307179586, step 0.01745329)
θ = 5.724679946541401 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
T: {{-sin(φ), cos(φ), 0, 0}, {-cos(φ) * cos(θ), -sin(φ) * cos(θ), sin(θ), 0}, {-cos(φ) * sin(θ), -sin(φ) * sin(θ), -cos(θ), ρ}, {0, 0, 0, 1}}
A: {4, 0, 0}
AH: {{Element[A, 1]}, {Element[A, 2]}, {Element[A, 3]}, {1}}
AT: T * AH
D = 10
A': (D * Element[AT, 1, 1] / Element[AT, 3, 1], D * Element[AT, 2, 1] / Element[AT, 3, 1])
B: {0, 0, 0}
B' = transf(ρ, φ, θ, B, D)
C: {0, 0, 2}
C' = transf(ρ, φ, θ, C, D)
D_1: {4, 0, 2}
D' = transf(ρ, φ, θ, D_1, D)
A'B'C'D', a', b', c', d' = Polygon(A', B', C', D')
E: {4, -3, 0}
F: {0, -3, 0}
G: {4, -3, 2}
H: {0, -3, 2}
E' = transf(ρ, φ, θ, E, D)
F' = transf(ρ, φ, θ, F, D)
G' = transf(ρ, φ, θ, G, D)
H' = transf(ρ, φ, θ, H, D)
A'D'G'E', a'_1, d'_1, g', e', a'_2 = Polygon(A', D', G', E', A')
D'G'H'C', d'_2, g'_1, h', c'_1 = Polygon(D', G', H', C')
F'E'G'H', f', e'_1, g'_2, h'_1 = Polygon(F', E', G', H')
B'C'H'F', b'_1, c'_2, h'_2, f'_1 = Polygon(B', C', H', F')
E'A, b'_2, c'_3, h'_3, f'_2 = Polygon(B', C', H', F')
E'A'B'F', e'_2, a'_3, b'_3, f'_3 = Polygon(E', A', B', F')

Tool: transf
trnasf(rho,phi,theta, KoordListe,D)
Input: ρ, φ, θ, A, D
Output: A'

T: {{-sin(φ), cos(φ), 0, 0}, {-cos(φ) * cos(θ), -sin(φ) * cos(θ), sin(θ), 0}, {-cos(φ) * sin(θ), -sin(φ) * sin(θ), -cos(θ), ρ}, {0, 0, 0, 1}}
A: {0, -3, 2}
AH: {{Element[A, 1]}, {Element[A, 2]}, {Element[A, 3]}, {1}}
AT: T * AH
A': (D * Element[AT, 1, 1] / Element[AT, 3, 1], D * Element[AT, 2, 1] / Element[AT, 3, 1])