From the free energy surfaces in G-p-T space a series of basic characteristics have beensummarized. For the reactions of most systems with phases of constant composition, eachof the surfaces should be approximate to a plane. After they meet, the points, curves andsurfaces possess distinct stability levels. Across the intersecting curves and points, the freeenergy surfaces and curves will change their stability levels. Linking invariant points ofdistinct stability levels, we can get various univariant curves differing in structure. Theangular extent between two univariant curves around the invariant points is less than 180°.The surfaces meeting in space and projecting onto the p-T section will give rise to partiallyclosed or open, rather than completely closed nets. Finally, based upon the basic characteristicsand criteria, we have derived the partially closed nets of n+3 and n+4 phases with maxi-mum closure by using geometrical and analytical methods. From the free energy surfaces in G-p-T space a series of basic characteristics have beensummarized. For the reactions of most systems with phases of constant composition, eachof the surfaces should be approximate to a plane. After they meet, the points, curves andsurfaces possess distinct stability levels. Across the intersecting curves and points, the freeenergy surfaces and curves will change their stability levels. Linking invariant points ofdistinct stability levels, we can get various univariant curves differing in structure. Theangular extent between two univariant curves around the invariant points is less than 180°.The surfaces meeting in space and projecting onto the p-T section will give rise to partiallyclosed or open, rather than completely closed nets. Finally, based upon the basic characteristicsand criteria, we have derived the partially closed nets of n+3 and n+4 phases with maxi-mum closure by using geometrical and analytical methods. From the free energy surfaces in GpT space a series of basic characteristics have beensummarized. For the reactions of most systems with phases of constant composition, eachof the surfaces should be approximate to a plane. After the free, the points, curves and surfaces of distinct distinct stability levels. Across the intersecting curves and points, the freeenergy surfaces and curves will change their stability levels. Linking invariant points ofdistinct stability levels, we can get various univariant curves differing in structure. Theangular extent between two univariant curves around the invariant points is less than 180 °. The surfaces meeting in space and projecting onto the pT section will give rise to partiallyclosed or open, rather than completely closed nets. Finally, based upon the basic characteristics and criteria, we have derived the partially closed nets of n + 3 and n +4 phases with maxi-mum closure by using geometrical and analytical methods. From the free energy surfaces in For the reactions of most systems with phases of constant composition, eachof the surfaces should be approximate to a plane. After the meet, the points, curves and surfaces have distinct stability levels. Across the intersecting curves and points, the freeenergy surfaces and curves will change their stability levels. Linking invariant points ofdistinct stability levels, we can get various univariant curves differing in structure. Theangular extent between two univariant curves around the invariant points is less than 180 °. The surfaces meeting in space and projecting onto the pT section will give rise to partiallyclosed or open, rather than completely closed nets. Finally, based upon the basic characteristics and criteria, we have derived the partially closed nets of n + 3 and n + 4 phases with maxi- mum closure by using geometrical and analytical methods.