编写程序：定义Point<T> get_low()函数来获得所有顶点坐标的下界。Point<T> get_high()函数来获得所有顶点坐标的上界。这两个点可以唯一组成一个多面体的最小包围盒。在Polyhedron类以及Facet类中各自定义一个T area()函数来返回一个多面体或者面片的表面积。T是模板定义的类型。Polyhedron的表面积就是他所有面片的面积之和。一个面片可能是个三角形，也可能包含多于三个顶点。为了简单起见，我们假设所有的面片都是凸多边形。在计算凸多边形的表面积的时候我们可以简单的将其进行三角化。假设一个Facet有N条边，每个顶点坐标为vertices[0], vertices[1]…vertices[N-1]。那这个多边形可以被三角化为N-2个三角形，分别是{vertices[0], vertices[1], vertices[2]}, {vertices[0], vertices[2], vertices[3]}、、、、{vertices[0], vertices[N-2], vertices[N-1]}。

以下是对应的 C++ 代码实现：

#include <iostream>
#include <vector>
#include <cmath>

using namespace std;

template<typename T>
struct Point {
    T x, y, z;
};

template<typename T>
class Facet {
public:
    Facet() = default;

    Facet(const vector<Point<T>>& vertices): vertices_(vertices) {}

    T area() const {
        T area = 0;
        for (int i = 2; i < vertices_.size(); i++) {
            Point<T> v1 = vertices_[i] - vertices_[0];
            Point<T> v2 = vertices_[i-1] - vertices_[0];
            Point<T> cross = cross_product(v1, v2);
            area += length(cross) / 2;
        }
        return area;
    }

private:
    vector<Point<T>> vertices_;

    Point<T> cross_product(const Point<T>& v1, const Point<T>& v2) const {
        Point<T> cross;
        cross.x = v1.y * v2.z - v1.z * v2.y;
        cross.y = v1.z * v2.x - v1.x * v2.z;
        cross.z = v1.x * v2.y - v1.y * v2.x;
        return cross;
    }

    T length(const Point<T>& p) const {
        return sqrt(p.x * p.x + p.y * p.y + p.z * p.z);
    }
};

template<typename T>
class Polyhedron {
public:
    Polyhedron() = default;

    Polyhedron(const vector<Facet<T>>& facets): facets_(facets) {}

    Point<T> get_low() const {
        Point<T> low = facets_[0].vertices_[0];
        for (const Facet<T>& facet : facets_) {
            for (const Point<T>& vertex : facet.vertices_) {
                low.x = min(low.x, vertex.x);
                low.y = min(low.y, vertex.y);
                low.z = min(low.z, vertex.z);
            }
        }
        return low;
    }

    Point<T> get_high() const {
        Point<T> high = facets_[0].vertices_[0];
        for (const Facet<T>& facet : facets_) {
            for (const Point<T>& vertex : facet.vertices_) {
                high.x = max(high.x, vertex.x);
                high.y = max(high.y, vertex.y);
                high.z = max(high.z, vertex.z);
            }
        }
        return high;
    }

    T area() const {
        T area = 0;
        for (const Facet<T>& facet : facets_) {
            area += facet.area();
        }
        return area;
    }

private:
    vector<Facet<T>> facets_;
};

int main() {
    vector<Point<double>> vertices1 = {{-1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
    Facet<double> facet1(vertices1);
    vector<Point<double>> vertices2 = {{0, 1, 0}, {1, 0, 0}, {0, 0, 1}};
    Facet<double> facet2(vertices2);
    vector<Facet<double>> facets = {facet1, facet2};
    Polyhedron<double> polyhedron(facets);

    Point<double> low = polyhedron.get_low();
    Point<double> high = polyhedron.get_high();
    cout << "Low: (" << low.x << ", " << low.y << ", " << low.z << ")" << endl;
    cout << "High: (" << high.x << ", " << high.y << ", " << high.z << ")" << endl;

    cout << "Area: " << polyhedron.area() << endl;
    return 0;
}

其中，Point 类表示一个三维点，Facet 类表示一个面片，Polyhedron 类表示一个多面体。在 Facet 类中，area 函数通过三角化计算凸多边形的表面积。在 Polyhedron 类中，get_low 和 get_high 函数分别计算多面体的顶点坐标的下界和上界，area 函数通过累加所有面片的面积计算多面体的表面积。