I asked Deepseek to draw the Schlegel diagram of a hexahedron — should be a very simple task right? Just 2 squares and link up their vertices. And yet I noticed something interesting: it tends to overthink and end up outputting nonsense answers when DeepThink is on (which is supposed to be more powerful and “clever”), but getting the task done correctly when DeepThink is off. Huh.

So this is the prompt I gave Deepseek:

draw the schlegel diagram of hexahedron with tikz

With DeepThink and Search (accessing internet), it “thought” for >15 minutes and gave me a complete trash:

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[scale=2]

% Define the vertices of the cube Schlegel diagram
% The cube has 8 vertices, but in Schlegel diagram we see 7 (one is "inside")

% Outer square (face 1)
\coordinate (A) at (0,0);
\coordinate (B) at (2,0);
\coordinate (C) at (2,2);
\coordinate (D) at (0,2);

% Inner vertices (the "back" face projected inside)
\coordinate (E) at (0.7,0.7);
\coordinate (F) at (1.3,0.7);
\coordinate (G) at (1.3,1.3);
\coordinate (H) at (0.7,1.3);

% Draw all edges
% Outer square (face 1)
\draw[thick] (A) -- (B) -- (C) -- (D) -- cycle;

% Inner square (face 2 - the "back" face)
\draw[thick] (E) -- (F) -- (G) -- (H) -- cycle;

% Connecting edges (the other 4 faces)
\draw[thick] (A) -- (E);
\draw[thick] (B) -- (F);
\draw[thick] (C) -- (G);
\draw[thick] (D) -- (H);

% Diagonal edges to show the 3D structure
\draw[thick] (E) -- (B);
\draw[thick] (F) -- (C);
\draw[thick] (G) -- (D);
\draw[thick] (H) -- (A);

% Label vertices
\node[below left] at (A) {A};
\node[below right] at (B) {B};
\node[above right] at (C) {C};
\node[above left] at (D) {D};
\node[below left] at (E) {E};
\node[below right] at (F) {F};
\node[above right] at (G) {G};
\node[above left] at (H) {H};

% Label faces
\node at (1,1) {Face 1 (Front)};
\node at (1,0.3) {Face 2 (Bottom)};
\node at (1.7,1) {Face 3 (Right)};
\node at (1,1.7) {Face 4 (Top)};
\node at (0.3,1) {Face 5 (Left)};
\node at (1,1) {Face 6 (Back)};

% Add a legend
\node[align=left, font=\small] at (3,1) {
    Schlegel Diagram of a Cube\\
    (Regular Hexahedron)\\
    \textbf{6 faces}\\
    \textbf{8 vertices}\\
    \textbf{12 edges}
};

\end{tikzpicture}

\end{document}

But without Deepthink and Search, it gave me a nice and clean (and correct!) solution:

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[scale=1.5]

% Define vertices for the cube Schlegel diagram
% Outer square (one face of the cube)
\coordinate (A) at (0,0);
\coordinate (B) at (3,0);
\coordinate (C) at (3,3);
\coordinate (D) at (0,3);

% Inner square (the opposite face projected inside)
\coordinate (E) at (1,1);
\coordinate (F) at (2,1);
\coordinate (G) at (2,2);
\coordinate (H) at (1,2);

% Draw all edges
% Outer face
\draw[thick] (A) -- (B) -- (C) -- (D) -- cycle;

% Inner face (back face)
\draw[thick] (E) -- (F) -- (G) -- (H) -- cycle;

% Connecting edges (the other 4 faces)
\draw[thick] (A) -- (E);
\draw[thick] (B) -- (F);
\draw[thick] (C) -- (G);
\draw[thick] (D) -- (H);

% Additional edges to complete the cube structure
\draw[thick] (A) -- (B);
\draw[thick] (B) -- (C);
\draw[thick] (C) -- (D);
\draw[thick] (D) -- (A);
\draw[thick] (E) -- (F);
\draw[thick] (F) -- (G);
\draw[thick] (G) -- (H);
\draw[thick] (H) -- (E);

% Draw vertices as dots
\foreach \point in {A,B,C,D,E,F,G,H}
    \filldraw (\point) circle (2pt);

% Label vertices
\node[below left] at (A) {1};
\node[below right] at (B) {2};
\node[above right] at (C) {3};
\node[above left] at (D) {4};
\node[below left] at (E) {5};
\node[below right] at (F) {6};
\node[above right] at (G) {7};
\node[above left] at (H) {8};

\end{tikzpicture}

\end{document}

Very weird. Perhaps it was due to 2 things:

  • it was genuinely overthinking, trying to make something profound while there is actually not much things there. (e.g. trying to add more “structures” to a very very simple schlegel diagram)
  • it “learned” things from the internet but it was just 鵜呑み (i.e. taking something withOUT a grain of salt. I’m not sure if there is a clean and short way to say it in english) so it added random craps into the answer.