Go: package main

import (
	"bufio"
	"os"
	"strconv"
	"strings"
		"reflect"
	"fmt"
)

var scanner = bufio.NewScanner(os.Stdin)

func main() {
	// 上面の色を固定してから、左右方向に回転して一致するものがあるかを調べる
	round := [][]int{
		{1,2,3,4,5,6}, {1,3,5,2,4,6}, {1,4,2,5,3,6}, {1,5,4,3,2,6}, // c1を上面に固定して回転
		{2,6,3,4,1,5}, {2,3,1,6,4,5}, {2,1,4,3,6,5}, {2,4,6,1,3,5}, // c2を上面に固定して回転
		{3,1,2,5,6,4}, {3,2,6,1,5,4}, {3,5,1,6,2,4}, {3,6,5,2,1,4}, // c3を上面に固定して回転
		{4,1,5,2,6,3}, {4,2,1,6,5,3}, {4,5,6,1,2,3}, {4,6,2,5,1,3}, // c4を上面に固定して回転
		{5,1,3,4,6,2}, {5,3,6,1,4,2}, {5,4,1,6,3,2}, {5,6,4,3,1,2}, // c5を上面に固定して回転
		{6,2,4,3,5,1}, {6,3,2,5,4,1}, {6,5,3,4,2,1}, {6,4,5,2,3,1}, // c6を上面に固定して回転

	}
	for scanner.Scan() {
		n, _ := strconv.Atoi(scanner.Text())
		if n == 0 {
			break
		}
		cubes := make([][]string, n)
		for i := 0; i < n; i++ {
			scanner.Scan()
			cubes[i] = strings.Split(scanner.Text(), " ")
		}
		check := func(a, b int) bool {
			tmp := make([]string, 6)
			for i := 0; i < 24; i++ {
				for j := 0; j < 6; j++ {
					tmp[j] = cubes[b][round[i][j]-1]
				}
				if reflect.DeepEqual(tmp, cubes[a]) {
					return true
				}
			}
			return false
		}
		tbl := make([]int, n)
		// 全ての組み合わせを調べる
		for i := 0; i < n; i++ {
			if tbl[i] == 1 {
				continue
			}
			for j := i+1; j < n; j++ {
				if check(i, j) {
					tbl[j] = 1
				}
			}
		}
		fmt.Println(sum(tbl))
	}
}

func sum(a []int) int {
	ret := 0
	for _, v := range a {
		ret += v
	}
	return ret
}

C++: 
// Trouble in Shinagawa's Artifacts
//  URL: http://rose.u-aizu.ac.jp/onlinejudge/ProblemSet/description.jsp?id=0198&lang=jp

#include <cstdio>
#include <cstring>
#include <vector>
#include <set>

// Ö
std::vector <int> rotate( std::vector <int> box, int a, int b, int c, int d );
std::vector <int> rotate_x( std::vector <int> box );
std::vector <int> rotate_y( std::vector <int> box );
std::vector <int> rotate_z( std::vector <int> box );

// ñ]
std::vector <int> rotate( std::vector <int> box, int a, int b, int c, int d )
{
	int tmp = box[a];
	box[a] = box[b];
	box[b] = box[c];
	box[c] = box[d];
	box[d] = tmp;

	return box;
}

// xÉñ]³¹éÖ
std::vector <int> rotate_x( std::vector <int> box )
{
	// xñ]
	// c1, c2, c3, c4, c5, c6 : default
	// c5, c1, c3, c4, c6, c2

	return rotate( box, 0, 4, 5, 1 );

}


// yÉñ]³¹éÖ
std::vector <int> rotate_y( std::vector <int> box )
{
	// yñ]
	// c1, c2, c3, c4, c5, c6 : default
	// c1, c4, c2, c5, c3, c6

	return rotate( box, 1, 3, 4, 2 );

}

// zÉñ]³¹éÖ
std::vector <int> rotate_z( std::vector <int> box )
{
	// zñ]
	// c1, c2, c3, c4, c5, c6 : default
	// c3, c2, c6, c1, c5, c4

	return rotate( box, 0, 2 ,5 ,3 );

}

// Gg[|Cg
int main()
{

	// Ï
	int n;
	int answer;
	char color[32];
	std::vector <int> box( 6, 0 );
	std::set < std::vector <int> > table;

	while( 1 )
	{
		// ú»
		answer = 0;
		table.clear();
		for( int i = 0; i < 6; ++i )
		{
			box[i] = 0;
		}

		// üÍ
		std::fflush( stdin );
		std::scanf( "%d", &n );

		// üÍÌIíèF[ÐÆÂ
		if( n == 0 ) break;

		// nÌ¾¯ÇÝÞ
		for( int i = 0; i < n; ++i )
		{
			std::fflush( stdin );

			// FîñðüÍ
			for( int j = 0; j < 6; ++j )
			{
				std::scanf( "%s", color );

				// µ¢â·¢æ¤É¶ñ¨®ÉÏ·
				// F: Red, Yellow, Blue, Magenta, Green, Cyan
				if( std::strcmp( "Red", color ) == 0 )
					box[j] = 1;
				else if( std::strcmp( "Yellow", color ) == 0 )
					box[j] = 2;
				else if( std::strcmp( "Blue", color ) == 0 )
					box[j] = 3;
				else if( std::strcmp( "Magenta", color ) == 0 )
					box[j] = 4;
				else if( std::strcmp( "Grdeen", color ) == 0 )
					box[j] = 5;
				else if( std::strcmp( "Cyan", color ) == 0 )
					box[j] = 6;
			}

			// insertÌOÉ¯¶àÌªÈ¢©T·
			// ¯¶àÌª Á½çJEg
			if( table.find( box ) != table.end() )
			{
				++answer;
				continue;
			}

			// insertµÄ¨­

				// x
				for( int j = 0; j < 4; ++j )
				{
					box = rotate_x( box );
					table.insert( box );
					for( int k = 0; k < 6; ++k )
					{
						if( k % 2 == 0 )
						{
							box = rotate_y( box );
							table.insert( box );
						}
						else
						{
							box = rotate_z( box );
							table.insert( box );
						}
					}
				}

				// x
				for( int j = 0; j < 4; ++j )
				{
					box = rotate_y( box );
					table.insert( box );
					for( int k = 0; k < 6; ++k )
					{
						if( k % 2 == 0 )
						{
							box = rotate_x( box );
							table.insert( box );
						}
						else
						{
							box = rotate_z( box );
							table.insert( box );
						}
					}
				}

				// x
				for( int j = 0; j < 4; ++j )
				{
					box = rotate_z( box );
					table.insert( box );
					for( int k = 0; k < 6; ++k )
					{
						if( k % 2 == 0 )
						{
							box = rotate_y( box );
							table.insert( box );
						}
						else
						{
							box = rotate_x( box );
							table.insert( box );
						}
					}
				}

		}

		// oÍ
		std::printf( "%d\n", answer );

	}

} // main()

C++: #include<bits/stdc++.h>
using namespace std;

struct BOX {
  string top;
  string back, left, right, head;
  string buttom;
  bool operator==(const BOX& b) const {
    return(top    == b.top   &&
           back   == b.back  &&
           left   == b.left  &&
           right  == b.right &&
           head   == b.head  &&
           buttom == b.buttom);
  }
};
class UnionFind{
private:
  vector< int > rank, p;
  void link(int x,int y){
    if(rank[x] > rank[y]){
      p[y] = x;
    }else{
      p[x] = y;
      if(rank[x] == rank[y]) rank[y]++;
    }
  }
public:
  UnionFind(int size){
    rank.resize(size,0);
    p.resize(size,0);
    for(int i = 0; i < rank.size(); i++){
      p[i] = i, rank[i] = 0;
    }
  }
  void Unite(int x,int y){
    if(Find(x) != Find(y)) link(Find(x),Find(y));
  }
  int Find(int x){
    return( x != p[x] ? p[x] = Find(p[x]) : p[x]);
  }
};

void Roll(BOX& B)
{
  string temp = B.head;
  B.head = B.right;
  B.right = B.back;
  B.back = B.left;
  B.left = temp;
}
 
void RoLL(BOX& B) {
  string temp = B.head;
  B.head = B.top;
  B.top = B.back;
  B.back = B.buttom;
  B.buttom = temp;
}
void RolL(BOX& B) {
  string temp = B.left;
  B.left = B.top;
  B.top = B.right;
  B.right = B.buttom;
  B.buttom = temp;
}
 
 
bool Myon(BOX& a, BOX& b)
{
  for(int k = 0; k < 4; k++) {
    Roll(a);
    for(int l = 0; l < 4; l++) {
      RoLL(a);
      for(int m = 0; m < 4; m++) {
        RolL(a);
        if(a == b) return(true);
      }
    }
  }
  return(false);
}

int main()
{
  int n;
  vector< BOX > boxes;
  while(cin >> n, n) {
    UnionFind uf(n);

    boxes.resize(n);
    int ret = 0;

    for(int i = 0; i < n; i++) {
      BOX &b = boxes[i];
      cin >> b.top >> b.head >> b.right >> b.left >> b.back >> b.buttom;
    }
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < n; j++) {
        if(Myon(boxes[i], boxes[j])) uf.Unite(i, j);
      }
    }
    for(int i = 0; i < n; i++) {
      ret += uf.Find(i) == i;
    }
    cout << n - ret << endl;
  }
}