I was designing this model with glasses.
The front triangle sides are $a, b$ and $c$. And the slant height is $h$.
The top length is $l$
and bottom full length is $L$.
One value that is fixed is the back side triangle angle i.e. $\,45\unicode{176}\,$ (forty-five degrees).
Now I need help to find relation between these values so I can design it for different value? Anyone can help me ?
Edited:
$x=45\unicode{176}$ (forty-five degrees) which is the front triangle slanted angle.
From the values of $c,h,l,L$ you can obtain the values of $a,b$, the height $H$ of the solid and the lengths of the sides of the back triangle.
The height of the solid is
$H=\sqrt{h^2-(L-l)^2}\;.$
The values of $a,b$ are
$a=\sqrt{h^2+(c-H)^2}\;,$
$b=\sqrt{2h^2-(L-l)^2}\;.$
The length of the side of the back triangle which forms the $45\unicode{176}$-angle with the base is $H\sqrt2$.
The length of the base is $c$.
The lenght of the other side is $\sqrt{H^2+(c-H)^2}$.
Addendum :
If we know that $x=45\unicode{176}$ (forty-five degrees) which is the front triangle slanted angle, then we can get all the lengths from $c,l,L$ in the following way :
$H=L-l$
$h=\sqrt2\big(L-l\big)$
$a=\sqrt{2(L-l)^2+(c+l-L)^2}\;,$
$b=\sqrt3\big(L-l\big)$
The length of the side of the back triangle which forms the $45\unicode{176}$-angle with the base is $\sqrt2\big(L-l\big)$.
The length of the base is $c$.
The length of the other side is
$\sqrt{(L-l)^2+(c+l-L)^2}\;.$