Here is my(=bad) translation of from the paper about Shklyaskiy by Golovina:

... in 1937/38 Dodik presented to school students a complete proof of Abel's theorem about equations of degree 5. He made geometric proof based on a note in the book of Hadamard, "From the existence of five cubes described in the exercise 1051, one can get nonexistence of solution in radicals to the general polynomial equations of degree five". The five cubes are the cubes inscribed in the dodecahedron...

Do you know any written proof based on this idea?

Here is my(=bad) translation of from the paper about Shklyarskiy by Golovina:

... in 1937/38 Dodik presented to school students a complete proof of Abel's theorem about equations of degree 5. He made geometric proof based on a note in the book of Hadamard, "From the existence of five cubes described in the exercise 1051, one can get nonexistence of solution in radicals to the general polynomial equations of degree five". The five cubes are the cubes inscribed in the dodecahedron...

Do you know any written proof based on this idea?

Here is my(=bad) translation of from the paper about Shklyaski by Golovina:

... in 1937/38 Dodik presented to school students a complete proof of Abel's theorem about equations of degree 5. He made geometric proof based on a note in the book of Hadamard, "From the existence of five cubes described in the exercise 1051, one can get nonexistence of solution in radicals to the general polynomial equations of degree five". The five cubes are the cubes inscribed in the dodecahedron...

Do you know any written proof based on this idea?

Here is my(=bad) translation of from the paper about Shklyaskiy by Golovina:

... in 1937/38 Dodik presented to school students a complete proof of Abel's theorem about equations of degree 5. He made geometric proof based on a note in the book of Hadamard, "From the existence of five cubes described in the exercise 1051, one can get nonexistence of solution in radicals to the general polynomial equations of degree five". The five cubes are the cubes inscribed in the dodecahedron...

Do you know any written proof based on this idea?