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3n",[578,1961,1963,1981],{"className":1962,"ariaHidden":608},[607],[578,1964,1966,1969,1972,1975,1978],{"className":1965},[612],[578,1967],{"className":1968,"style":617},[616],[578,1970,642],{"className":1971,"style":657},[621,622],[578,1973],{"className":1974,"style":791},[752],[578,1976,725],{"className":1977},[795],[578,1979],{"className":1980,"style":791},[752],[578,1982,1984,1987,1990],{"className":1983},[612],[578,1985],{"className":1986,"style":977},[616],[578,1988,914],{"className":1989},[621],[578,1991,1864],{"className":1992},[621,622],[578,1994,1996,2018],{"className":1995},[581],[578,1997,1999],{"className":1998},[585],[587,2000,2001],{"xmlns":589},[591,2002,2003,2015],{},[594,2004,2005,2007,2009,2011,2013],{},[597,2006,676],{},[713,2008,725],{},[597,2010,1864],{},[713,2012,720],{},[727,2014,729],{},[601,2016,2017],{"encoding":603},"F = n + 2",[578,2019,2021,2039,2058],{"className":2020,"ariaHidden":608},[607],[578,2022,2024,2027,2030,2033,2036],{"className":2023},[612],[578,2025],{"className":2026,"style":617},[616],[578,2028,676],{"className":2029,"style":691},[621,622],[578,2031],{"className":2032,"style":791},[752],[578,2034,725],{"className":2035},[795],[578,2037],{"className":2038,"style":791},[752],[578,2040,2042,2046,2049,2052,2055],{"className":2041},[612],[578,2043],{"className":2044,"style":2045},[616],"height:0.6667em;vertical-align:-0.0833em;",[578,2047,1864],{"className":2048},[621,622],[578,2050],{"className":2051,"style":753},[752],[578,2053,720],{"className":2054},[757],[578,2056],{"className":2057,"style":753},[752],[578,2059,2061,2064],{"className":2060},[612],[578,2062],{"className":2063,"style":977},[616],[578,2065,729],{"className":2066},[621],". Es ergibt sich ",[578,2069,2071,2105],{"className":2070},[581],[578,2072,2074],{"className":2073},[585],[587,2075,2076],{"xmlns":589},[591,2077,2078,2102],{},[594,2079,2080,2082,2084,2086,2088,2090,2092,2094,2096,2098,2100],{},[727,2081,729],{},[597,2083,1864],{},[713,2085,715],{},[727,2087,914],{},[597,2089,1864],{},[713,2091,720],{},[597,2093,1864],{},[713,2095,720],{},[727,2097,729],{},[713,2099,725],{},[727,2101,729],{},[601,2103,2104],{"encoding":603},"2n - 3n + n + 2 = 2",[578,2106,2108,2129,2150,2168,2186],{"className":2107,"ariaHidden":608},[607],[578,2109,2111,2114,2117,2120,2123,2126],{"className":2110},[612],[578,2112],{"className":2113,"style":940},[616],[578,2115,729],{"className":2116},[621],[578,2118,1864],{"className":2119},[621,622],[578,2121],{"className":2122,"style":753},[752],[578,2124,715],{"className":2125},[757],[578,2127],{"className":2128,"style":753},[752],[578,2130,2132,2135,2138,2141,2144,2147],{"className":2131},[612],[578,2133],{"className":2134,"style":940},[616],[578,2136,914],{"className":2137},[621],[578,2139,1864],{"className":2140},[621,622],[578,2142],{"className":2143,"style":753},[752],[578,2145,720],{"className":2146},[757],[578,2148],{"className":2149,"style":753},[752],[578,2151,2153,2156,2159,2162,2165],{"className":2152},[612],[578,2154],{"className":2155,"style":2045},[616],[578,2157,1864],{"className":2158},[621,622],[578,2160],{"className":2161,"style":753},[752],[578,2163,720],{"className":2164},[757],[578,2166],{"className":2167,"style":753},[752],[578,2169,2171,2174,2177,2180,2183],{"className":2170},[612],[578,2172],{"className":2173,"style":977},[616],[578,2175,729],{"className":2176},[621],[578,2178],{"className":2179,"style":791},[752],[578,2181,725],{"className":2182},[795],[578,2184],{"className":2185,"style":791},[752],[578,2187,2189,2192],{"className":2188},[612],[578,2190],{"className":2191,"style":977},[616],[578,2193,729],{"className":2194},[621],[565,2196,2197,2200,2201,2229,2230,2258,2259,2311],{},[569,2198,2199],{},"Fußball:"," Er besteht aus ",[578,2202,2204,2217],{"className":2203},[581],[578,2205,2207],{"className":2206},[585],[587,2208,2209],{"xmlns":589},[591,2210,2211,2215],{},[594,2212,2213],{},[727,2214,1266],{},[601,2216,1266],{"encoding":603},[578,2218,2220],{"className":2219,"ariaHidden":608},[607],[578,2221,2223,2226],{"className":2222},[612],[578,2224],{"className":2225,"style":977},[616],[578,2227,1266],{"className":2228},[621]," Fünfecken und ",[578,2231,2233,2246],{"className":2232},[581],[578,2234,2236],{"className":2235},[585],[587,2237,2238],{"xmlns":589},[591,2239,2240,2244],{},[594,2241,2242],{},[727,2243,1614],{},[601,2245,1614],{"encoding":603},[578,2247,2249],{"className":2248,"ariaHidden":608},[607],[578,2250,2252,2255],{"className":2251},[612],[578,2253],{"className":2254,"style":977},[616],[578,2256,1614],{"className":2257},[621]," Sechsecken, also ",[578,2260,2262,2281],{"className":2261},[581],[578,2263,2265],{"className":2264},[585],[587,2266,2267],{"xmlns":589},[591,2268,2269,2278],{},[594,2270,2271,2273,2275],{},[597,2272,676],{},[713,2274,725],{},[727,2276,2277],{},"32",[601,2279,2280],{"encoding":603},"F = 32",[578,2282,2284,2302],{"className":2283,"ariaHidden":608},[607],[578,2285,2287,2290,2293,2296,2299],{"className":2286},[612],[578,2288],{"className":2289,"style":617},[616],[578,2291,676],{"className":2292,"style":691},[621,622],[578,2294],{"className":2295,"style":791},[752],[578,2297,725],{"className":2298},[795],[578,2300],{"className":2301,"style":791},[752],[578,2303,2305,2308],{"className":2304},[612],[578,2306],{"className":2307,"style":977},[616],[578,2309,2277],{"className":2310},[621],". Jede Kante gehört zu zwei Flächen, daher ist",[578,2313,2315],{"className":2314},[696],[578,2316,2318,2362],{"className":2317},[581],[578,2319,2321],{"className":2320},[585],[587,2322,2323],{"xmlns":589,"display":705},[591,2324,2325,2359],{},[594,2326,2327,2329,2331,2354,2356],{},[597,2328,642],{},[713,2330,725],{},[2332,2333,2334,2352],"mfrac",{},[594,2335,2336,2338,2341,2344,2346,2348,2350],{},[727,2337,1266],{},[713,2339,2340],{},"⋅",[727,2342,2343],{},"5",[713,2345,720],{},[727,2347,1614],{},[713,2349,2340],{},[727,2351,1297],{},[727,2353,729],{},[713,2355,725],{},[727,2357,2358],{},"90",[601,2360,2361],{"encoding":603},"K = \\frac{12 \\cdot 5 + 20 \\cdot 6}{2} = 90",[578,2363,2365,2383,2515],{"className":2364,"ariaHidden":608},[607],[578,2366,2368,2371,2374,2377,2380],{"className":2367},[612],[578,2369],{"className":2370,"style":617},[616],[578,2372,642],{"className":2373,"style":657},[621,622],[578,2375],{"className":2376,"style":791},[752],[578,2378,725],{"className":2379},[795],[578,2381],{"className":2382,"style":791},[752],[578,2384,2386,2390,2506,2509,2512],{"className":2385},[612],[578,2387],{"className":2388,"style":2389},[616],"height:2.0074em;vertical-align:-0.686em;",[578,2391,2393,2398,2502],{"className":2392},[621],[578,2394],{"className":2395},[2396,2397],"mopen","nulldelimiter",[578,2399,2401],{"className":2400},[2332],[578,2402,2406,2493],{"className":2403},[2404,2405],"vlist-t","vlist-t2",[578,2407,2410,2488],{"className":2408},[2409],"vlist-r",[578,2411,2415,2429,2440],{"className":2412,"style":2414},[2413],"vlist","height:1.3214em;",[578,2416,2418,2423],{"style":2417},"top:-2.314em;",[578,2419],{"className":2420,"style":2422},[2421],"pstrut","height:3em;",[578,2424,2426],{"className":2425},[621],[578,2427,729],{"className":2428},[621],[578,2430,2432,2435],{"style":2431},"top:-3.23em;",[578,2433],{"className":2434,"style":2422},[2421],[578,2436],{"className":2437,"style":2439},[2438],"frac-line","border-bottom-width:0.04em;",[578,2441,2443,2446],{"style":2442},"top:-3.677em;",[578,2444],{"className":2445,"style":2422},[2421],[578,2447,2449,2452,2455,2458,2461,2464,2467,2470,2473,2476,2479,2482,2485],{"className":2448},[621],[578,2450,1266],{"className":2451},[621],[578,2453],{"className":2454,"style":753},[752],[578,2456,2340],{"className":2457},[757],[578,2459],{"className":2460,"style":753},[752],[578,2462,2343],{"className":2463},[621],[578,2465],{"className":2466,"style":753},[752],[578,2468,720],{"className":2469},[757],[578,2471],{"className":2472,"style":753},[752],[578,2474,1614],{"className":2475},[621],[578,2477],{"className":2478,"style":753},[752],[578,2480,2340],{"className":2481},[757],[578,2483],{"className":2484,"style":753},[752],[578,2486,1297],{"className":2487},[621],[578,2489,2492],{"className":2490},[2491],"vlist-s","​",[578,2494,2496],{"className":2495},[2409],[578,2497,2500],{"className":2498,"style":2499},[2413],"height:0.686em;",[578,2501],{},[578,2503],{"className":2504},[2505,2397],"mclose",[578,2507],{"className":2508,"style":791},[752],[578,2510,725],{"className":2511},[795],[578,2513],{"className":2514,"style":791},[752],[578,2516,2518,2521],{"className":2517},[612],[578,2519],{"className":2520,"style":977},[616],[578,2522,2358],{"className":2523},[621],[565,2525,2526,2527,2711,2712,1028],{},"Mit dem Polyedersatz folgt ",[578,2528,2530,2573],{"className":2529},[581],[578,2531,2533],{"className":2532},[585],[587,2534,2535],{"xmlns":589},[591,2536,2537,2570],{},[594,2538,2539,2541,2543,2545,2547,2549,2551,2553,2555,2557,2559,2561,2563,2565,2567],{},[597,2540,599],{},[713,2542,725],{},[727,2544,729],{},[713,2546,720],{},[597,2548,642],{},[713,2550,715],{},[597,2552,676],{},[713,2554,725],{},[727,2556,729],{},[713,2558,720],{},[727,2560,2358],{},[713,2562,715],{},[727,2564,2277],{},[713,2566,725],{},[727,2568,2569],{},"60",[601,2571,2572],{"encoding":603},"E = 2 + K - F = 2 + 90 - 32 = 60",[578,2574,2576,2594,2612,2630,2648,2666,2684,2702],{"className":2575,"ariaHidden":608},[607],[578,2577,2579,2582,2585,2588,2591],{"className":2578},[612],[578,2580],{"className":2581,"style":617},[616],[578,2583,599],{"className":2584,"style":623},[621,622],[578,2586],{"className":2587,"style":791},[752],[578,2589,725],{"className":2590},[795],[578,2592],{"className":2593,"style":791},[752],[578,2595,2597,2600,2603,2606,2609],{"className":2596},[612],[578,2598],{"className":2599,"style":940},[616],[578,2601,729],{"className":2602},[621],[578,2604],{"className":2605,"style":753},[752],[578,2607,720],{"className":2608},[757],[578,2610],{"className":2611,"style":753},[752],[578,2613,2615,2618,2621,2624,2627],{"className":2614},[612],[578,2616],{"className":2617,"style":745},[616],[578,2619,642],{"className":2620,"style":657},[621,622],[578,2622],{"className":2623,"style":753},[752],[578,2625,715],{"className":2626},[757],[578,2628],{"className":2629,"style":753},[752],[578,2631,2633,2636,2639,2642,2645],{"className":2632},[612],[578,2634],{"className":2635,"style":617},[616],[578,2637,676],{"className":2638,"style":691},[621,622],[578,2640],{"className":2641,"style":791},[752],[578,2643,725],{"className":2644},[795],[578,2646],{"className":2647,"style":791},[752],[578,2649,2651,2654,2657,2660,2663],{"className":2650},[612],[578,2652],{"className":2653,"style":940},[616],[578,2655,729],{"className":2656},[621],[578,2658],{"className":2659,"style":753},[752],[578,2661,720],{"className":2662},[757],[578,2664],{"className":2665,"style":753},[752],[578,2667,2669,2672,2675,2678,2681],{"className":2668},[612],[578,2670],{"className":2671,"style":940},[616],[578,2673,2358],{"className":2674},[621],[578,2676],{"className":2677,"style":753},[752],[578,2679,715],{"className":2680},[757],[578,2682],{"className":2683,"style":753},[752],[578,2685,2687,2690,2693,2696,2699],{"className":2686},[612],[578,2688],{"className":2689,"style":977},[616],[578,2691,2277],{"className":2692},[621],[578,2694],{"className":2695,"style":791},[752],[578,2697,725],{"className":2698},[795],[578,2700],{"className":2701,"style":791},[752],[578,2703,2705,2708],{"className":2704},[612],[578,2706],{"className":2707,"style":977},[616],[578,2709,2569],{"className":2710},[621],". Kontrolle: An jeder Ecke stoßen drei Flächen zusammen, also ",[578,2713,2715,2742],{"className":2714},[581],[578,2716,2718],{"className":2717},[585],[587,2719,2720],{"xmlns":589},[591,2721,2722,2739],{},[594,2723,2724,2726,2728,2735,2737],{},[597,2725,599],{},[713,2727,725],{},[2332,2729,2730,2733],{},[727,2731,2732],{},"180",[727,2734,914],{},[713,2736,725],{},[727,2738,2569],{},[601,2740,2741],{"encoding":603},"E = \\frac{180}{3} = 60",[578,2743,2745,2763,2855],{"className":2744,"ariaHidden":608},[607],[578,2746,2748,2751,2754,2757,2760],{"className":2747},[612],[578,2749],{"className":2750,"style":617},[616],[578,2752,599],{"className":2753,"style":623},[621,622],[578,2755],{"className":2756,"style":791},[752],[578,2758,725],{"className":2759},[795],[578,2761],{"className":2762,"style":791},[752],[578,2764,2766,2770,2846,2849,2852],{"className":2765},[612],[578,2767],{"className":2768,"style":2769},[616],"height:1.1901em;vertical-align:-0.345em;",[578,2771,2773,2776,2843],{"className":2772},[621],[578,2774],{"className":2775},[2396,2397],[578,2777,2779],{"className":2778},[2332],[578,2780,2782,2834],{"className":2781},[2404,2405],[578,2783,2785,2831],{"className":2784},[2409],[578,2786,2789,2808,2816],{"className":2787,"style":2788},[2413],"height:0.8451em;",[578,2790,2792,2795],{"style":2791},"top:-2.655em;",[578,2793],{"className":2794,"style":2422},[2421],[578,2796,2802],{"className":2797},[2798,2799,2800,2801],"sizing","reset-size6","size3","mtight",[578,2803,2805],{"className":2804},[621,2801],[578,2806,914],{"className":2807},[621,2801],[578,2809,2810,2813],{"style":2431},[578,2811],{"className":2812,"style":2422},[2421],[578,2814],{"className":2815,"style":2439},[2438],[578,2817,2819,2822],{"style":2818},"top:-3.394em;",[578,2820],{"className":2821,"style":2422},[2421],[578,2823,2825],{"className":2824},[2798,2799,2800,2801],[578,2826,2828],{"className":2827},[621,2801],[578,2829,2732],{"className":2830},[621,2801],[578,2832,2492],{"className":2833},[2491],[578,2835,2837],{"className":2836},[2409],[578,2838,2841],{"className":2839,"style":2840},[2413],"height:0.345em;",[578,2842],{},[578,2844],{"className":2845},[2505,2397],[578,2847],{"className":2848,"style":791},[752],[578,2850,725],{"className":2851},[795],[578,2853],{"className":2854,"style":791},[752],[578,2856,2858,2861],{"className":2857},[612],[578,2859],{"className":2860,"style":977},[616],[578,2862,2569],{"className":2863},[621],[560,2865,2867],{"id":2866},"typische-fehler","Typische Fehler",[2869,2870,2871,2907,3053],"ul",{},[2872,2873,2874,2877,2878,2906],"li",{},[569,2875,2876],{},"Kanten doppelt zählen."," Wer bei jeder Fläche die Seiten zählt und addiert, zählt jede Kante zweimal. Man muss durch ",[578,2879,2881,2894],{"className":2880},[581],[578,2882,2884],{"className":2883},[585],[587,2885,2886],{"xmlns":589},[591,2887,2888,2892],{},[594,2889,2890],{},[727,2891,729],{},[601,2893,729],{"encoding":603},[578,2895,2897],{"className":2896,"ariaHidden":608},[607],[578,2898,2900,2903],{"className":2899},[612],[578,2901],{"className":2902,"style":977},[616],[578,2904,729],{"className":2905},[621]," teilen.",[2872,2908,2909,2912,2913,2916,2917,2920,2921,2994,2995,3024,3025,1028],{},[569,2910,2911],{},"Vorzeichen vertauschen."," Es heißt Ecken ",[569,2914,2915],{},"minus"," Kanten ",[569,2918,2919],{},"plus"," Flächen. ",[578,2922,2924,2946],{"className":2923},[581],[578,2925,2927],{"className":2926},[585],[587,2928,2929],{"xmlns":589},[591,2930,2931,2943],{},[594,2932,2933,2935,2937,2939,2941],{},[597,2934,599],{},[713,2936,720],{},[597,2938,642],{},[713,2940,715],{},[597,2942,676],{},[601,2944,2945],{"encoding":603},"E + K - F",[578,2947,2949,2967,2985],{"className":2948,"ariaHidden":608},[607],[578,2950,2952,2955,2958,2961,2964],{"className":2951},[612],[578,2953],{"className":2954,"style":745},[616],[578,2956,599],{"className":2957,"style":623},[621,622],[578,2959],{"className":2960,"style":753},[752],[578,2962,720],{"className":2963},[757],[578,2965],{"className":2966,"style":753},[752],[578,2968,2970,2973,2976,2979,2982],{"className":2969},[612],[578,2971],{"className":2972,"style":745},[616],[578,2974,642],{"className":2975,"style":657},[621,622],[578,2977],{"className":2978,"style":753},[752],[578,2980,715],{"className":2981},[757],[578,2983],{"className":2984,"style":753},[752],[578,2986,2988,2991],{"className":2987},[612],[578,2989],{"className":2990,"style":617},[616],[578,2992,676],{"className":2993,"style":691},[621,622]," ergibt beim Würfel ",[578,2996,2998,3012],{"className":2997},[581],[578,2999,3001],{"className":3000},[585],[587,3002,3003],{"xmlns":589},[591,3004,3005,3010],{},[594,3006,3007],{},[727,3008,3009],{},"14",[601,3011,3009],{"encoding":603},[578,3013,3015],{"className":3014,"ariaHidden":608},[607],[578,3016,3018,3021],{"className":3017},[612],[578,3019],{"className":3020,"style":977},[616],[578,3022,3009],{"className":3023},[621],", nicht ",[578,3026,3028,3041],{"className":3027},[581],[578,3029,3031],{"className":3030},[585],[587,3032,3033],{"xmlns":589},[591,3034,3035,3039],{},[594,3036,3037],{},[727,3038,729],{},[601,3040,729],{"encoding":603},[578,3042,3044],{"className":3043,"ariaHidden":608},[607],[578,3045,3047,3050],{"className":3046},[612],[578,3048],{"className":3049,"style":977},[616],[578,3051,729],{"className":3052},[621],[2872,3054,3055,3058,3059,3088,3089,3117,3118,3146,3147,3243],{},[569,3056,3057],{},"Körper mit Loch."," Bei einem Rahmen mit einem Tunnel, etwa aus ",[578,3060,3062,3076],{"className":3061},[581],[578,3063,3065],{"className":3064},[585],[587,3066,3067],{"xmlns":589},[591,3068,3069,3074],{},[594,3070,3071],{},[727,3072,3073],{},"16",[601,3075,3073],{"encoding":603},[578,3077,3079],{"className":3078,"ariaHidden":608},[607],[578,3080,3082,3085],{"className":3081},[612],[578,3083],{"className":3084,"style":977},[616],[578,3086,3073],{"className":3087},[621]," Ecken, ",[578,3090,3092,3105],{"className":3091},[581],[578,3093,3095],{"className":3094},[585],[587,3096,3097],{"xmlns":589},[591,3098,3099,3103],{},[594,3100,3101],{},[727,3102,2277],{},[601,3104,2277],{"encoding":603},[578,3106,3108],{"className":3107,"ariaHidden":608},[607],[578,3109,3111,3114],{"className":3110},[612],[578,3112],{"className":3113,"style":977},[616],[578,3115,2277],{"className":3116},[621]," Kanten und ",[578,3119,3121,3134],{"className":3120},[581],[578,3122,3124],{"className":3123},[585],[587,3125,3126],{"xmlns":589},[591,3127,3128,3132],{},[594,3129,3130],{},[727,3131,3073],{},[601,3133,3073],{"encoding":603},[578,3135,3137],{"className":3136,"ariaHidden":608},[607],[578,3138,3140,3143],{"className":3139},[612],[578,3141],{"className":3142,"style":977},[616],[578,3144,3073],{"className":3145},[621]," Flächen, gilt ",[578,3148,3150,3177],{"className":3149},[581],[578,3151,3153],{"className":3152},[585],[587,3154,3155],{"xmlns":589},[591,3156,3157,3174],{},[594,3158,3159,3161,3163,3165,3167,3169,3171],{},[597,3160,599],{},[713,3162,715],{},[597,3164,642],{},[713,3166,720],{},[597,3168,676],{},[713,3170,725],{},[727,3172,3173],{},"0",[601,3175,3176],{"encoding":603},"E - K + F = 0",[578,3178,3180,3198,3216,3234],{"className":3179,"ariaHidden":608},[607],[578,3181,3183,3186,3189,3192,3195],{"className":3182},[612],[578,3184],{"className":3185,"style":745},[616],[578,3187,599],{"className":3188,"style":623},[621,622],[578,3190],{"className":3191,"style":753},[752],[578,3193,715],{"className":3194},[757],[578,3196],{"className":3197,"style":753},[752],[578,3199,3201,3204,3207,3210,3213],{"className":3200},[612],[578,3202],{"className":3203,"style":745},[616],[578,3205,642],{"className":3206,"style":657},[621,622],[578,3208],{"className":3209,"style":753},[752],[578,3211,720],{"className":3212},[757],[578,3214],{"className":3215,"style":753},[752],[578,3217,3219,3222,3225,3228,3231],{"className":3218},[612],[578,3220],{"className":3221,"style":617},[616],[578,3223,676],{"className":3224,"style":691},[621,622],[578,3226],{"className":3227,"style":791},[752],[578,3229,725],{"className":3230},[795],[578,3232],{"className":3233,"style":791},[752],[578,3235,3237,3240],{"className":3236},[612],[578,3238],{"className":3239,"style":977},[616],[578,3241,3173],{"className":3242},[621],". Der Satz gilt nur für Polyeder ohne Löcher.",{"title":3245,"searchDepth":3246,"depth":3246,"links":3247},"",2,[3248,3249,3250],{"id":562,"depth":3246,"text":563},{"id":1031,"depth":3246,"text":1032},{"id":2866,"depth":3246,"text":2867},[3252,3254,3256,3258,3260,3262,3264,3266,3268,3270,3272,3274,3276],{"lhs":3253,"rhs":729},"8 - 12 + 6",{"lhs":3255,"rhs":729},"4 - 6 + 4",{"lhs":3257,"rhs":729},"6 - 12 + 8",{"lhs":3259,"rhs":729},"20 - 30 + 12",{"lhs":3261,"rhs":729},"12 - 30 + 20",{"lhs":3263,"rhs":729},"2*n - 3*n + (n + 2)",{"lhs":3265,"rhs":2277},"12 + 20",{"lhs":3267,"rhs":2358},"(12*5 + 20*6)\u002F2",{"lhs":3269,"rhs":2569},"2 + 90 - 32",{"lhs":3271,"rhs":2569},"(12*5 + 20*6)\u002F3",{"lhs":3273,"rhs":3173},"16 - 32 + 16",{"lhs":3275,"rhs":3009},"8 + 12 - 6",{"lhs":3277,"rhs":923},"3 - 3 + 1","\\text{konvexes Polyeder (allgemein: Polyeder ohne Löcher)}","\u003Cspan class=\"katex\">konvexes Polyeder (allgemein: Polyeder ohne Löcher)\u003C\u002Fspan>",null,"md","euler-polyhedron","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>E\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>K\u003C\u002Fmi>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>F\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E - K + F = 2\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.7667em;vertical-align:-0.0833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">K\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">+\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Feulerscher-polyedersatz",[],[3290,3291,3292],"handshake-lemma","polygon-angle-sum","prism-surface",{"title":548,"description":3245},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Feulerscher-polyedersatz","Bei jedem konvexen Polyeder ergibt Ecken minus Kanten plus Flächen immer 2.",[3297,3298,3299,3300],"polyeder","ecken kanten flächen","körper","eulersche polyederformel",[3302,3305,3308],{"symbol":599,"meaning":3303,"symbolHtml":3304},"Anzahl der Ecken","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>E\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">E\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">E\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":642,"meaning":3306,"symbolHtml":3307},"Anzahl der Kanten","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>K\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">K\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">K\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":676,"meaning":3309,"symbolHtml":3310},"Anzahl der Flächen","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>F\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","ynVT6Av188cvy5SYDStSVv2Ir5XvpfxSFXAkQaF3PRc",[3313,3316,3319],{"stem":3314,"title":3315,"category":187},"de\u002Fformulas\u002Fmath\u002Fdiscrete-math\u002Fhandschlaglemma","Handschlaglemma",{"stem":3317,"title":3318,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Finnenwinkelsumme-vieleck","Innenwinkelsumme im Vieleck",{"stem":3320,"title":3321,"category":247},"de\u002Fformulas\u002Fmath\u002Fgeometry\u002Foberflaeche-prisma","Oberfläche eines Prismas",1793824276159]