Here is a layout of the design I had in mind:

// Vertex: class to act as a vector. Maybe named inappropriately, but whatever.
public class Vertex{

	// Store the fields of the vector
	private double x, y, z;
	
	// Constructor. Sets the members
	Vertex( double _x, double _y, double _z );

	// Return X
	double getX();

	// Return Y
	double getY();

	// Return Z
	double getZ();

	// Normalize the vector
	void Normalize();

	// Return the dotproduct of this and who
	double dotproduct( Vertex who );

	// Translates the vector. Maybe this should be a generic matrix multiplication.
	// Will be changed in next version
	void Move( double mx, double my, double mz );

	// Returns a copy of this object
	Vertex copy();
}

// Edge: stores two vertexes
public class Edge{

	// Vertex 1, 2, and the color they should be
	private Vertex v1;
	private Vertex v2;
	private Color color;

	// Constructor sets the data members
	Edge( Vertex p1, Vertex p2, Color _color );

	// Returns a copy of this object
	Edge copy();

	// Draws a line between the two vertexes using a Camera object
	void Draw( Camera cam, int p1, int p2 );

	// Returns a vertex which is the average of the other 2 vertexes
	Vertex Average();

	// Translates the two vertexes
	void Move( double mx, double my, double mz ){
	
}

// Face: stores multiple edges
public class Face{

	// List of edges
	private Vector edge_list;
	
	// Constructor initializes the edge_list
	Face();

	// Adds an edge to the list
	void addEdge( Edge who );

	// Draws the edges
	void Draw( Camera cam, int who );

	// Returns an average vertex of all other edge averages
	Vertex Average();

	// Translates all edges
	void Move( double mx, double my, double mz );

	// Returns a copy of this object
	Face copy();
}

// Obj3d: Stores multiple faces
public class Obj3d{

	// start : Vertex that object should move away from
	private Vertex start;
	// explode: How far the object should be from start
	private double explode;
	// face_list: list of faces
	private Vector face_list;

	// Constructor: sets the starting point and initializes the list
	Obj3d( Vertex _start );
	
	// Adds a face to the list
	void addFace( Face who );
	
	// Draws all the faces and the light lines
	void Draw( Camera cam );

	// Returns an average of all the faces
	Vertex Average();
	
	// Sets the exploding factor
	void Explode( double f );
	
}

// Camera: stores all information about graphics and matrix math
public class Camera{

	// position vector
	private Vertex pos;
	
	// front, top, and right vectors of the camera
	private Vertex front, top, right;

	// personal graphics variable
	private Graphics graphic;

	// focal length of the camera
	private double epsilon;

	// Constructor: sets the position vector
	Camera( Vertex v );

	// sets the graphics to the supplied graphics
	void setGraphics( Graphics g );

	// Returns the graphics owned by the camera
	Graphics getGraphics();

	// Calculates the right and top vectors given a position.
	void Reset();
	
	// Rotates the camera around the X,Y,Z axis.
	void Rotate( double x, double y, double z );

	// Moves the camera in the direction of the front vector
	void Thrust( double m ){

	// Returns a 2d projection of a 3d coordinate in space
	Vertex vertex2d( Vertex d_3 );
		
}