菱形是一種具有很多特殊性質的圖形，由菱形組成的多面體自然有很多有趣的應用。本文重點研究了三種菱形多面體，即菱形十二面體、菱形二十面體和菱形三十面體，並探討了以下主題：
1. 以菱形多面體的拼圖的著色。
2. 菱形多面體的分割。
3. 菱形多面體與其分割的連桿結構。

The rhombus is a kind of figure with many special properties, and the polyhedron composed of rhombuses naturally has many interesting applications. This paper focus on three rhombic polyhedra: the rhombic dodecahedron, rhombic icosahedron and rhombic triacontahedron and explores the following topics :
1. Colorings of the "Jupiter", a 3D jigsaw puzzle based on the
rhombic polyhedron
2. Dissection-assembly of the rhombic polyhedron
3. Linkage associated with dissection-assembly of the rhombic polyhedron

1 Introduction 4
1.1 Research Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Rhombic Dodecahedron, Rhombic Triacontahedron and Rhombic Icosahedron . . . . . . . . . . 4
2 Jupiter, a Puzzle Based on the Rhombic Triacontahedron 6
2.1 The Third Stellation of Rhombic Dodecahedron . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Colorings of the Puzzle Based on the Third Stellation of Rhombic Dodecahedron . . . . . 9
2.2 The Puzzle Based on the Rhombic Triacontahedron . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Colorings of Jupiter of Rhombic Triacontahedron . . . . . . . . . . . . . . . . . . . . . . 14
3 Dissection of the Rhombic Polyhedron 20
3.1 Dissection-Assembly of the Rhombic Dodecahedron into 4 Rhombohedra . . . . . . . . . . . . . 20
3.2 Dissection-Assembly of the Rhombic Icosahedron into 10 Rhombohedra . . . . . . . . . . . . . . 21
3.3 Dissection-Assembly of the Rhombic Triacontahedron into 20 Rhombohedra . . . . . . . . . . . 24
4 Linkage Associated with the Rhombic Polyhedron 26
4.1 Assembly of 4 Rhombohedra Linkages to form the Rhombic Dodecahedron Linkage . . . . . . . 26
4.2 Assembly of 10 Rhombohedra Linkages to form the Rhombic Icosahedron Linkage . . . . . . . . 27
4.3 Assembly of 20 Rhombohedra Linkages to form the Rhombic Triacontahedron Linkage . . . . . . 28
References 30

[1] H. Martyn Cundy \& A. P. Rollett, Mathematical Model, Oxford University Press, 1961

[2] KANAYAMA, R. Bibliography on linkage. Tohoku Mathematical Journal, First Series, 1933, 37: 294-319.

[3] Stewart T. Coffin, The Puzzling World of Polyhedral Dissections, Oxford University Press, 1974

[4] Stewart T. Coffin, Geometric puzzle design, A K Peters, Wellesley Massachusetts, 2007