\begin{definition}
Un \MotDefinition{solide}{} est un objet en relief.\\ On ne peut pas le tracer en vraie grandeur sur une feuille de papier plane.
\end{definition}
\begin{remarques}
\begin{itemize}
\item Un \MotDefinition{patron}{} permet de {\bfseries fabriquer} le solide par pliage.
\item La \MotDefinition{perspective cavalière}{} permet de représenter le solide sur une feuille papier en donnant l'impression de la 3D.
%On peut  {\bfseries fabriquer} le solide en construisant un \MotDefinition{patron}{}, que %l'on découpe, plie et colle.
%\item On peut  {\bfseries représenter} le solide sur une feuille plane en donnant l'impression de la 3D. Nous utiliserons, par exemple  la \MotDefinition{perspective cavalière}{} (voir % schéma ci\nobreakdash-contre).
\end{itemize}
\end{remarques}
\begin{center}
\begin{tikzpicture}[general, scale=0.5]
\draw[fill=J4, color=J4] (2,2)--(6,2)--(6,6)--(2,6)--cycle;
\draw[fill=F4] (0,0)--(4,0)--(4,4)--(0,4)--cycle;  
\draw (0,4)--(2,6)--(6,6)--(4,4);
\draw (6,6)--(6,2)--(4,0);
\draw[dashed] (2,2)--(6,2);
\draw[dashed, G1, tres epais] (2,2)--(2,6);
\draw[dashed, G1, tres epais] (2,2)--(0,0);
\draw[color=C1, dashed, epais] (4.8,0)--(7,0);
\draw[fill=C1, color=C1] (4.8,0) arc (0:45:0.8)--(4,0)--cycle;
\draw[color=C1] (5,0.4) node[right] {\bfseries angle de fuite};
\draw[ H1prime, tres epais] (4,4)--(6,6);
\draw[ H1prime, tres epais] (4,0)--(6,2);
\draw[ G1, tres epais] (0,4)--(2,6);
\draw[color=G1, ->, epais] (-2,3) to[bend left] (2,3); %arête arrière
\draw[color=G1, ->, epais] (-2,0.5) to[bend left] (1,1); %arête protée par une fuyante
\draw[color=G1, ->, epais] (-2,5.5)to[bend left](1,5);%arête visible
\draw[color=J1, ->, epais] (3,7)to[bend left](3.5,5); %face arrière
\draw[color=F1, ->, epais] (2,-1)to[bend left](2.5,1); %face frontale
\draw[color=H1prime, ->, epais] (8.5,4.5)to[bend right](5,5);
\draw[color=H1prime, ->, epais] (8.5,3.5)to[bend left](5,1);
\draw[color=G1] (-2,3.3) node[left] {\bfseries arête};
\draw[color=G1] (-2,2.7) node[left] {\bfseries non visible};
\draw[color=G1] (-2,1.1) node[left] {\bfseries arête portée};
\draw[color=G1] (-2,0.5) node[left] {\bfseries par une fuyante};
\draw[color=G1] (-2,-0.1) node[left] {\bfseries en grandeur};
\draw[color=G1] (-2,-0.7) node[left] {\bfseries réduite};
\draw[color=G1] (-2,6) node[left] {\bfseries arête};
\draw[color=G1] (-2,5.4) node[left] {\bfseries visible};
\draw[color=J1] (3,7) node[above] {\bfseries face arrière};
\draw[color=F1] (2,-1) node[below] {\bfseries face frontale};
\draw[color=F1] (2,-1.6) node[below] {\bfseries en vraie grandeur};
\draw[color=H1prime] (8.5,6.1) node[right] {\bfseries deux droites};
\draw[color=H1prime] (8.5,5.5) node[right] {\bfseries parallèles dans};
\draw[color=H1prime] (8.5,4.9) node[right] {\bfseries la réalité sont};
\draw[color=H1prime] (8.5,4.3) node[right] {\bfseries représentées};
\draw[color=H1prime] (8.5,3.7) node[right] {\bfseries par des};
\draw[color=H1prime] (8.5,3.1) node[right] {\bfseries parallèles en};
\draw[color=H1prime] (8.5,2.5) node[right] {\bfseries perspective};
\draw[color=H1prime] (8.5,1.9) node[right] {\bfseries cavalière};
\end{tikzpicture}
\end{center}

\begin{tabular}{!{\color{G2}\vline width 2pt}
m{0.49\linewidth}m{0.49\linewidth}!{\color{G2}\vline width 2pt}}
\arrayrulecolor{G2}
\doublerulesepcolor{G2}
\hline\hline
\arrayrulecolor{gray}
\doublerulesepcolor{white}
\cellcolor{G3}{\bfseries Parallélépipède rectangle} & \cellcolor{FondTableaux} Le patron est composé de rectangles.  \\%\cline{1-1}
\rowcolor{FondTableaux}$\mathcal{V}= \mbox{largeur}\times \mbox{hauteur}\times\mbox{profondeur}$ & L'aire d'un rectangle est: $\mathcal{A}=\mbox{Longueur} \times \mbox{largeur}$\\%\hline
\begin{tikzpicture}[general, scale=0.8] %pavé perspective
\draw[fill=F4] (-0.5,-1)-- (4,-1)--(4,1)--(-0.5,1)--cycle;
\draw[fill=J3]  (4,-1)--(5,-0.5)--(5,1.5)--(4,1)--cycle;
\draw[fill=H3] (-0.5,1)-- (4,1)--(5,1.5)--(0.5,1.5)--cycle;
\draw (-0.5,1)-- (4,1);
\draw (4,1)-- (4,-1);
\draw [dashed] (0.5,1.5)-- (0.5,-0.5);
\draw [dashed] (0.5,-0.5)-- (-0.5,-1);
\draw [dashed] (0.5,-0.5)-- (5,-0.5);
%\draw (3.3,1.05) node[below, color=F1] {\bfseries largeur};
\draw (1.75,-1.1) node[above, color=F1] {\bfseries  longueur};
\draw[color=F1, tres epais] (-0.5,-1)--(4,-1);
\draw (4.25,0.25) node[rotate=-90.0, color=G1] {\bfseries  hauteur};
\draw[color=G1, tres epais] (4,-1)--(4,1);
%\draw (5,-0.65) node[rotate=26.5, color=C1] {\bfseries profondeur};
\draw (4.65,-0.94) node[rotate=29, color=C1] {\bfseries  largeur};
\draw[color=C1, tres epais] (5,-0.5)--(4,-1);
\end{tikzpicture}
&
\begin{tikzpicture}[general, scale=0.6] %pavé patron
\clip (-0.1,-0.1) rectangle (10,4.6);
\draw[fill=J3, color=J3] (0,0)-- (1.5,0)--(1.5,1)--(0,1)--cycle;
\draw[fill=J3, color=J3] (0,3.5)-- (1.5,3.5)--(1.5,4.5)--(0,4.5)--cycle;
\draw[fill=F3, color=F3] (2.5,1)-- (4,1)--(4,3.5)--(2.5,3.5)--cycle;
\draw[fill=F3, color=F3] (0,1)-- (1.5,1)--(1.5,3.5)--(0,3.5)--cycle;
\draw[fill=H3, color=H3] (4,1)-- (5,1)--(5,3.5)--(4,3.5)--cycle;
\draw[fill=H3, color=H3] (1.5,1)-- (2.5,1)--(2.5,3.5)--(1.5,3.5)--cycle;

\draw[color=F1, epais] (4,1)--(4,3.5);
\draw[color=F1, epais]  (1.5,1)--(1.5,3.5);
\draw[color=F1, epais] (0,1)-- (0,3.5);
\draw[color=F1, epais] (2.5,1)--(2.5,3.5);
\draw[color=F1, epais] (5,1)--(5,3.5);
\draw[color=C1, epais]  (1.5,0)--(1.5,1);
\draw[color=C1, epais] (0,0)--(0,1);
\draw[color=C1, epais] (1.5,3.5)--(1.5,4.5);
\draw[color=C1, epais] (0,3.5)-- (0,4.5);
\draw[color=C1, epais] (2.5,3.5)--(1.5,3.5);
\draw[color=C1, epais] (1.5,1)-- (2.5,1);
\draw[color=C1, epais] (4,1)-- (5,1);
\draw[color=C1, epais] (5,3.5)--(4,3.5);
\draw[color=G1, epais] (0,0)-- (1.5,0);
\draw[color=G1, epais] (1.5,3.5)--(0,3.5);
\draw[color=G1, epais] (1.5,1)--(0,1);
\draw[color=G1, epais] (2.5,1)-- (4,1);
\draw[color=G1, epais] (1.5,4.5)--(0,4.5);
\draw[color=G1, epais] (4,3.5)--(2.5,3.5);
\draw (5.5,2.5) node[right] {\bfseries \it Les segments};
\draw (5.5,2) node[right] {\bfseries \it de la même couleur};
\draw (5.5,1.5) node[right] {\bfseries \it ont  même mesure};
\end{tikzpicture}
\\
\arrayrulecolor{G2}
\doublerulesepcolor{G2}
\hline\hline
\arrayrulecolor{gray}
\doublerulesepcolor{white} 
\cellcolor{G3}{\bfseries Pyramides}
&\cellcolor{FondTableaux}Le patron est composé d'un polygone et de triangles. \\\rowcolor{FondTableaux}
$\mathcal{V}=\left(\mbox{Aire de la base}\times \mbox{hauteur}\right)\div 3$&L'aire d'un triangle est: $\mathcal A = \left(\mbox{base}\times \mbox{hauteur}\right)\div 2$\\%\hline
\begin{tikzpicture}[general, scale=0.55]%pyramide perspective
\draw[fill=C4] (0.62,-2)-- (4.12,-2)--(-0.6,1.76)--cycle;
\draw[fill=J4] (5,-0.84)-- (4.12,-2)-- (-0.6,1.76)--cycle;
\draw [dashed] (-0.6,1.76)-- (1.38,-0.8);
\draw [dashed] (1.38,-0.8)-- (0.62,-2);
\draw [dashed] (1.38,-0.8)-- (5,-0.84);
%%%%hauteur
\draw [fill=C2] (-0.8,-1.3) rectangle (-1.1,-1);
\draw [dashed] (-0.6,1.76)-- (-1.6,1.76);
\draw [dashed] (1.3,-1.3)-- (-1.6,-1.3);
\draw [dashed] (-0.8,-1.3)-- (-0.8,1.76);
 \draw (-1.1,0.2) node[rotate=90] {hauteur};
\end{tikzpicture}
&
\begin{tikzpicture}[general, xscale=0.6,yscale=0.4] %pyramide patron
\draw[fill=J4] (4.18,1.2)-- (5.02,2.6)-- (8.46,2.08)--cycle;
\draw[fill=C4] (0.56,1.2)-- (0.36,-1.03)-- (4.18,1.2);
\draw[fill=B4]  (0.56,1.22)-- (-1.17,2.67)-- (1.4,2.6);
\draw[fill=B4] (1.4,2.6)-- (2.52,4.97)-- (5.02,2.6);
\draw[fill=B4] (1.4,2.6)--(5.02,2.6)--(4.18,1.2)--(0.56,1.2)--cycle;

 \draw[color=A1] (2.2,0.1) node {{\boldmath $\int$}};
 \draw[color=A1] (6,1.6) node {{\boldmath $\int$}};
 \draw[color=A1] (0.45,0.1) node {{\boldmath $\infty$}};
 \draw[color=A1] (-0.2,1.85) node[rotate=60] {{\boldmath $\infty$}};
 \draw[color=A1] (1.95,3.8) node[rotate=50] {{\boldmath $\ddagger$}};
 \draw[color=A1] (0.2,2.65) node {{\boldmath $\ddagger$}};
 \draw[color=A1] (3.8,3.8) node[rotate=50] {{\boldmath $\approx$}};
 \draw[color=A1] (6.4,2.35) node[rotate=85] {{\boldmath $\approx$}};
\end{tikzpicture}
\\\arrayrulecolor{G2}
\doublerulesepcolor{G2}
\hline\hline
\arrayrulecolor{gray}
\doublerulesepcolor{white} 
\cellcolor{G3}{\bfseries Cylindre de révolution}& \cellcolor{FondTableaux}Le patron est composé d'un rectangle et de deux
\\
\rowcolor{FondTableaux}$\mathcal{V}=\mbox{Aire de la base}\times \mbox{hauteur}$& disques. L'aire d'un disque est: $\mathcal A = \pi \times  \mbox{rayon}^2$\\
\begin{tikzpicture}[general, xscale=0.5,yscale=0.6]%cylindre perspective
 \draw[fill=B4, color=B4] (0,0)--(0,3)--(5,3)--(5,0)-- cycle;
 \draw[fill=B3] (0,3) .. controls +(0,-0.5) and +(0,-0.5)..(5,3);
 \draw[fill=B3] (0,3) .. controls +(0,0.5) and +(0,0.5)..(5,3); 
 \draw[color=B3, line cap=butt] (0,3)--(5,3); 
 \draw[fill=B3] (0,0) .. controls +(0,-0.5) and +(0,-0.5)..(5,0);
 \draw[dashed,fill=B3] (0,0) .. controls +(0,0.5) and +(0,0.5)..(5,0); 
 \draw[color=B3] (0,0) --(5,0);
\draw[fill=A1, color=A1]  (2.5,0) rectangle (2.25,0.25);
 \draw[dashed, color=C1] (2.5,0)--(0,0);
 \draw (-0.5,0) node[left, color=C1] {\bfseries rayon};
 \draw[->, color=C1] (-0.5,0)--(0,0);
 \draw[dashed, color=A1] (2.5,3)--(2.5,0);
 \draw[color=A1] (2.5,3) node {{\boldmath $-$}};
 \draw (2.8,1.4) node[rotate=-90, color=A1] {\bfseries hauteur}; 
 \draw (0,0)--(0,3);
  \draw (5,3)--(5,0);

 \end{tikzpicture}
 &\begin{tikzpicture}[general, xscale=0.6,yscale=0.6] %cylindre patron
%  \draw[fill=B3] (0,0) circle (1);
 \draw[color=J1, fill=B3, epais] (0,0) circle (1);
 \draw[fill=B3] (7,0) circle (1);
 \draw[fill=B4] (1,-1.5)--(6,-1.5)--(6,2.5)--(1,2.5)--cycle;
 \draw[dashed, color=C1] (0,0)--(-1,0);
 \draw (-1.5,0) node[left, color=C1] {\bfseries rayon};
 \draw[->, color=C1] (-1.5,0)--(-1,0);
 \draw (1.7,0.5) node[rotate=-90, J1] {\bfseries circonférence};
 \draw (1.3,0.5) node[rotate=-90, J1] {\bfseries de la base};
 \draw (3.2,2.2) node[color=A1] {\bfseries hauteur};
 \draw[color=A1,  epais] (6,2.5)--(1,2.5);
 \draw[color=J1, epais] (1,-1.5)--(1,2.5);
 \end{tikzpicture}
\\\arrayrulecolor{G2}
\doublerulesepcolor{G2}
\hline\hline
 \end{tabular}

\begin{tabular}{!{\color{G2}\vline width 2pt}
m{0.49\linewidth}m{0.49\linewidth}!{\color{G2}\vline width 2pt}
}\arrayrulecolor{G2}
\doublerulesepcolor{G2}
\hline\hline
\arrayrulecolor{gray}
\doublerulesepcolor{white} 
\cellcolor{G3}{\bfseries Cône de révolution} & \cellcolor{FondTableaux}Le patron est composé d'un disque et d'une portion de
\\
\rowcolor{FondTableaux}$\mathcal{V}=\mbox{Aire de la base}\times \mbox{hauteur}\div 3$& disque avec $\alpha=\mbox{rayon}\div\mbox{génératrice}\times 360$\degre\\
\begin{tikzpicture}[general, scale=0.5] %cone perspective
 \draw[fill=H4] (0,0)--(2.5,3)--(5,0);
 \draw[fill=H2] (0,0) .. controls +(0,-0.5) and +(0,-0.5)..(5,0);
 \draw[dashed,fill=H2] (0,0) .. controls +(0,0.5) and +(0,0.5)..(5,0); 
 \draw[ color=H2] (0,0)--(5,0);
 \draw[dashed, color=J1] (0,0)--(2.5,0);
 \draw[dashed, color=C1] (2.5,3)--(2.5,0);
 \draw[->, color=J1] (-0.5,0)--(0,0);
 \draw (-0.5,0) node[left, color=J1] {\bfseries rayon};
 \draw[color=A1, epais] (2.5,3)--(5,0);
 \draw (4.2,1.6) node[rotate=-50, color=A1] {\bfseries génératrice};
 \draw (2.8,1.3) node[rotate=-90, color=C1] {\bfseries hauteur};
\draw [color=C1, fill=C1] (2.5,0) rectangle (2.25,0.25);
\end{tikzpicture}&\begin{tikzpicture}[general, scale=0.55]%cone patron
\clip (-4,-2.2) rectangle (7.2,2.2);
 \draw[fill=H2] (0,0) circle (1);
 \draw[fill=H4] (5,0) arc (0:250:2)--(3,0)--cycle;
\draw[fill=A1, color=A1] (3.4,0) arc (0:250:0.4)--(3,0)--cycle;
 \draw[dashed, color=J1] (0,0)--(-1,0);
 \draw (-1.5,0) node[left, color=J1] {\bfseries rayon};
 \draw[->, color=J1] (-1.5,0)--(-1,0);
 \draw (3,0) node[below right, color=A1] {\bfseries génératrice};
 \draw[color=A1, epais] (3,0)--(5,0);
 \draw (2.5,0.5) node[color=A1] {{\boldmath $\alpha$}};
\end{tikzpicture}
\\\arrayrulecolor{G2}
\doublerulesepcolor{G2}
\hline\hline
\arrayrulecolor{gray}
\doublerulesepcolor{white} 
\cellcolor{G3}{\bfseries Sphère et boule}&
\cellcolor{FondTableaux}\parbox{\linewidth}{$\mathcal{V}=\dfrac{\TopStrut 4}{\BotStrut 3}\pi\times  \mbox{rayon}^3$  \hfill $\mathcal{A}=4\times \pi \times \mbox{rayon}^2$}
%\\\arrayrulecolor{G2}
%\doublerulesepcolor{G2}
%\hline\hline
\\%\hline
\begin{tikzpicture}[general, scale=0.4]
\clip (-3,-2.55)rectangle(7.5,2.775);
 \draw[fill=A4] (2.5,0) circle (2.5);
 \draw[color=A3] (0,0)--(5,0);
 \draw[fill=A3] (0,0) .. controls +(0,-0.5) and +(0,-0.5)..(5,0);
 \draw[dashed,fill=A3] (0,0) .. controls +(0,0.5) and +(0,0.5)..(5,0); 
 \draw[dashed, color=A1] (0,0)--(2.5,0);
 \draw (-0.5,0) node[color=A1, left] {\bfseries rayon};
 \draw[color=A1, ->]  (-0.5,0)--(0,0);
\end{tikzpicture}
&
La sphère n'a pas de patron. \\
\arrayrulecolor{G2}
\doublerulesepcolor{G2}
\hline\hline
\arrayrulecolor{gray}
\doublerulesepcolor{white} 
\end{tabular}
