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style=\"font-size:1.25em\">\u003Cstrong>\u003Cspan style=\"color:#0000ff\">正多面体は、全部でいくつある？\u003C\u002Fspan>\u003C\u002Fstrong>\u003C\u002Fspan>\n \nいくつかのパーツを貼り合わせて真球に近づけようとするとき、正多角形を貼り付けるのがよいと考えるのは極めて自然な発想です。\n \nじゃあ、正多面体は何種類存在するのでしょうか。\nこれ、以下の、たったの\u003Cspan style=\"font-size:1.25em\">\u003Cstrong>5種類\u003C\u002Fstrong>\u003C\u002Fspan>だけ。\n \n\u003Cstrong>\u003Cspan style=\"color:#ff0000\">正三角形×4枚＝正四面体\n正方形×6枚＝正六面体（立方体）\n正三角形×8枚＝正八面体\n正五角形×12枚＝正十二面体\n正三角形×20枚＝正20面体 \u003C\u002Fspan>\u003C\u002Fstrong>\n\nそんなの常識だというなら、ちゃんと証明しましょう。\n\n\u003Cspan style=\"font-size:1.25em\">\u003Cspan style=\"color:#0000ff\">大学入試だけじゃなく、中学入試にも出ます！\u003C\u002Fspan>\u003C\u002Fspan>\n\nこれらを証明する問題は、時々\u003Cstrong>大学入試\u003C\u002Fstrong>にもでますが、\n（\u003Cstrong>オイラーの多面体定理\u003C\u002Fstrong>とか…理系の受験生ならわかってますね。）\n \nなんだ、大学入試の話と思ったあなた、実はこの証明問題は、\n\u003Cstrong>中学入試\u003C\u002Fstrong>でも取り上げられることがあるんです。\nしかも、オイラーの多面体定理を使ってというひとことでかたづけずに、\nなぜ、\n\n\u003Cstrong>頂点の数－辺の数＋面の数＝2\u003C\u002Fstrong>\n\nが成り立つかを考えさせて、頂点の数や面の数、多面体の展開図などから理詰めで5種類に絞り込んでいったり、\n\u003Cstrong>内角の和の大きさ\u003C\u002Fstrong>から、正六角形以上の多面体が作れないことを示したりと\nむしろ高校数学以上かもしれない難易度を小学生に突きつけるのです。\n\n（この項、後編に続く）",{"show_cv_flg":458,"caption_cv":459,"type_cv":460,"display_image_cv":445},true,"他の多面体についても知りたい人や、図形が大の苦手という人",{"key":461,"label":462},"inquiry","お問い合わせ",{"show_telephone_flg":458,"display_image_telephone":445},false,{"topics_id":466,"ymd":467,"contents_type":439,"subject":468,"topics_flg":441,"open_flg":441,"regular_flg":442,"inst_ymdhi":443,"update_ymdhi":443,"topics_group_id":444,"slug":445,"group_nm":446,"group_description":445,"contents_type_cnt":441,"contents_type_nm":446,"contents_type_slug":445,"contents_type_parent_nm":432,"category_parent_id":432,"contents_type_ext_col_01":445,"contents_type_ext_col_02":445,"contents_type_ext_col_03":445,"contents_type_ext_col_04":445,"contents_type_ext_col_05":445,"tags":469,"contents_type_list":470,"prefecture_name":128,"school_name":449,"sid":450,"school_cd":451,"image":471,"rotation_angle":442,"main_text":475,"setting_cv":476,"setting_telephone":479,"pickup_flg":464},353902,"2021-11-02","中学入試レベル？　大学入試レベル？　\nサッカーボールを使った図形の学び方　～後編～",[],[439],{"id":472,"url":473,"desc":445,"url_org":474},"353902_ext_08_0","https:\u002F\u002Faxis-web-cms.g.kuroco-img.app\u002Fv=1774188537\u002Ffiles\u002Ftopics\u002F353902_ext_8_0.jpg","https:\u002F\u002Faxis-web-cms.g.kuroco-img.app\u002Ffiles\u002Ftopics\u002F353902_ext_8_0.jpg","こんにちは！　湘南深沢校責任者の水谷活士です。\n \n前回はサッカーボールを手掛かりに、正多面体について考えてみました。\n\u003Cstrong>正多面体は正二十面体どまり\u003C\u002Fstrong>なので、サッカーボールの話の戻ると、\nそのままでは、球体には程遠いことは一目瞭然ですね。\n \nより球体に近づけるために（かはわかりませんが？！）二つの\u003Cstrong>正多角形を組み合わせた多面体\u003C\u002Fstrong>を考えた人がいました。アディダスの職人さんではありません。\nはるか古の天才数学者\u003Cstrong>\u003Cspan style=\"color:#ff0000\">アルキメデス\u003C\u002Fspan>\u003C\u002Fstrong>です。\n今でも主に体育の現場などでみられるカタチのサッカーボールは、よく見ると正五角形と正六角形の組み合わせでできていることがわかります。面の数は全部で\u003Cstrong>\u003Cspan style=\"color:#ff0000\">32\u003C\u002Fspan>\u003C\u002Fstrong>。\n構造的には、正二十面体の頂点をスパッと切り落として整えたものです。\n \nこの多面体は、\u003Cstrong>半正多面体\u003C\u002Fstrong>（かつては\u003Cstrong>準正多面体\u003C\u002Fstrong>とも）のひとつで、正多角形が3種類組み合わさったものを含め、\u003Cstrong>全部で\u003Cspan style=\"color:#ff0000\">13種類\u003C\u002Fspan>\u003C\u002Fstrong>あります。（詳しい定義は調べてね！）\n \nあ～、図形は苦手、これ以上ムリ！ と考えているあなた、\nじゃあ、読むのはやめて、実際に、正多面体を作ってみましょう。\nまず、方眼紙とハサミを用意しましょう。\nヒマな時間にパズルゲームをするノリで、最初は、\u003Cstrong>正多面体\u003Cspan style=\"color:#ff0000\">5種類\u003C\u002Fspan>\u003C\u002Fstrong>\u003Cspan style=\"color:#ff0000\">から\u003C\u002Fspan>。\nそう、展開図を作るんです。\n面倒なら\u003Cstrong>立方体\u003C\u002Fstrong>（\u003Cstrong>サイコロ\u003C\u002Fstrong>ですね）を手始めに。\n\u003Cstrong>\u003Cspan style=\"color:#0000ff\">展開図の答えは\u003C\u002Fspan>\u003Cspan style=\"color:#ff0000\">1\u003C\u002Fspan>\u003Cspan style=\"color:#0000ff\">種類とは限りませんよ\u003C\u002Fspan>\u003C\u002Fstrong>。\nちなみに立方体は\u003Cspan style=\"color:#ff0000\">\u003Cstrong>11種類\u003C\u002Fstrong>\u003C\u002Fspan>の展開図があります。\n\n混乱しそうなときは、\u003Cstrong>各面を色塗り\u003C\u002Fstrong>したり、\u003Cstrong>各辺にナンバリング\u003C\u002Fstrong>してみましょう！\n\u003Cstrong>どの頂点が合わさるか\u003C\u002Fstrong>を考えるのもコツのひとつです。\nうまくいかないときは、複数枚を\u003Cstrong>切り張りすることから\u003C\u002Fstrong>始めてもいいでしょう。\n\nわかっている方には何をいまさらですが、\u003Cstrong>方眼紙だけでは正三角形は作図できません\u003C\u002Fstrong>。正四面体や正八面体、正二十面体の展開図の作図にはコンパスや分度器等が必要です。見取図であれば方眼紙だけでもなんとかいけるかもしれませんが…。\n \nうまくいったら、いよいよサッカーボールの展開図に挑戦です。\n\u003Cstrong>正六角形\u003Cspan style=\"color:#ff0000\">20\u003C\u002Fspan>+正五角形\u003Cspan style=\"color:#ff0000\">12\u003C\u002Fspan>\u003C\u002Fstrong>でできていますが、正二十面体の展開図をアレンジすることが成功への近道です。\n\u003Cstrong>五角形の周りには\u003Cspan style=\"color:#ff0000\">5つ\u003C\u002Fspan>の六角形\u003C\u002Fstrong>と考えるか、\n\u003Cstrong>五角形\u003Cspan style=\"color:#ff0000\">1つ\u003C\u002Fspan>と六角形\u003Cspan style=\"color:#ff0000\">2つ\u003C\u002Fspan>の組合わせの\u003C\u002Fstrong>集合体と考えるか…。\n写真の展開図の\u003Cstrong>どこにどう五角形を加えればいいか\u003C\u002Fstrong>…。\n \nさぁ、楽しんで！　",{"show_cv_flg":458,"caption_cv":477,"type_cv":478,"display_image_cv":445},"図形が大っ嫌いな人も、大っ好きな人も、興味がわいたひと",{"key":461,"label":462},{"show_telephone_flg":458,"display_image_telephone":445},{"topics_id":481,"ymd":482,"contents_type":439,"subject":483,"topics_flg":441,"open_flg":441,"regular_flg":442,"inst_ymdhi":443,"update_ymdhi":443,"topics_group_id":444,"slug":445,"group_nm":446,"group_description":445,"contents_type_cnt":441,"contents_type_nm":446,"contents_type_slug":445,"contents_type_parent_nm":432,"category_parent_id":432,"contents_type_ext_col_01":445,"contents_type_ext_col_02":445,"contents_type_ext_col_03":445,"contents_type_ext_col_04":445,"contents_type_ext_col_05":445,"tags":484,"contents_type_list":485,"prefecture_name":128,"school_name":449,"sid":450,"school_cd":451,"image":486,"rotation_angle":442,"main_text":490,"setting_cv":491,"setting_telephone":494,"pickup_flg":464},353904,"2021-10-08","定期試験が終わったら、さぁ、どうする？",[],[439],{"id":487,"url":488,"desc":445,"url_org":489},"353904_ext_08_0","https:\u002F\u002Faxis-web-cms.g.kuroco-img.app\u002Fv=1774188538\u002Ffiles\u002Ftopics\u002F353904_ext_8_0.jpg","https:\u002F\u002Faxis-web-cms.g.kuroco-img.app\u002Ffiles\u002Ftopics\u002F353904_ext_8_0.jpg","みなさん、こんにちは\n湘南深沢校の水谷活士です。\n\n2学期最初の定期試験が終わった生徒も多い湘南深沢校ですが、\n\n\u003Cspan style=\"font-size:1.25em\">\u003Cspan style=\"color:#ff0000\">\u003Cstrong>試験→答案返却→解き直し→課題提出→面談\u003C\u002Fstrong>\u003C\u002Fspan>\u003C\u002Fspan>\n\nという流れに、ただ身を任せていると、なんだか、\n\n\u003Cspan style=\"color:#000000\">\u003Cstrong>試験が終わったこと＝（イコール）出来たこと、解ったこと、知ってること\u003C\u002Fstrong>\u003C\u002Fspan>\n\nに勝手に置き換えてしまうことが間々あります。\n素晴らしいプラス思考、毎日ハッピーで過ごせそう！\nというわけにはいきませんよね。\nこれはあまりやってほしくないことです。\n\n同じプラス思考でも、\n間違いだらけの結果を見て、\n\n\u003Cspan style=\"color:#fff0f5\">\u003Cstrong>\u003Cspan style=\"background-color:#ff0000\">“自分の間違いが分かってよかった”\u003C\u002Fspan>\n\u003Cspan style=\"background-color:#ff0000\">“自分のできるところとできないところがはっきりしてすっきりした！”\u003C\u002Fspan>\u003C\u002Fstrong>\u003C\u002Fspan>\n\nこんなふうに思えたら、復習、解き直しも楽しくなりますよね。\n\n\u003Cstrong>勘がさえてて、当てずっぽうで答えた問題が、たまたま大当たりして、\n満点が取れて大満足！\nだから見直しなんて必要ないよ！\u003C\u002Fstrong>\n\nこれも、次の満点がどこにも保障されてないことから目を背けてますね。\n\n\u003Cstrong>\u003Cspan style=\"color:#ff0000\">勘で当たったところをホントの実力にするために、しっかりやり直して次に臨む。\u003C\u002Fspan>\u003C\u002Fstrong>\n\nこれが\u003Cspan style=\"color:#fff0f5\">\u003Cspan style=\"background-color:#ff0000\">ホントの前向き思考\u003C\u002Fspan>\u003C\u002Fspan>です！\n\n\u003Cstrong>今回は50点だったけど、友達より5点よかったからOK！ とか\n前回より1点少ないだけだから許容範囲！\u003C\u002Fstrong>\n\nなんていう不思議なマイルールを毎回作っちゃうあなたも、\u003Cspan style=\"color:#fff0f5\">\u003Cspan style=\"background-color:#000000\">なんちゃってポジティブシンキング\u003C\u002Fspan>\u003C\u002Fspan>ですよね。\n\n他人や過去の自分と比較することは、時にはとても大切ですが、目の前の現実から逃れる手段に使うことは、お勧めできません。なんの解決にもなっていないからです。\n\n\u003Cstrong>\u003Cspan style=\"font-size:1.25em\">\u003Cspan style=\"color:#ff0000\">じゃあ、どうすればいいの！\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fstrong>\n\nそんなあなたのために、\nこの教室には\u003Cstrong>たくさんの先生が答えを用意して待っています。\u003C\u002Fstrong>\n\n\u003Cstrong>期末試験はホントのプラス思考を身につけよう！\u003C\u002Fstrong>\n\n\n ",{"show_cv_flg":458,"caption_cv":492,"type_cv":493,"display_image_cv":445},"ホントのプラス思考で試験前も後も過ごしたいと思った人",{"key":461,"label":462},{"show_telephone_flg":458,"display_image_telephone":445},{"topics_id":496,"contents_type":497,"subject":449,"topics_flg":441,"open_flg":441,"regular_flg":442,"inst_ymdhi":498,"update_ymdhi":499,"topics_group_id":500,"slug":445,"order_no":501,"group_nm":502,"group_description":503,"contents_type_cnt":441,"contents_type_nm":504,"contents_type_slug":432,"contents_type_parent_nm":432,"category_parent_id":432,"contents_type_ext_col_01":432,"contents_type_ext_col_02":432,"contents_type_ext_col_03":432,"contents_type_ext_col_04":432,"contents_type_ext_col_05":432,"tags":505,"contents_type_list":506,"sid":450,"school_cd":451,"school_id":507,"school_slug":508,"division_cd":127,"sub_area":445,"postal_cd":509,"prefecture":510,"address1":511,"address2":512,"city_cd":513,"telephone":514,"accept_time":515,"parking":518,"transportations":521,"access":525,"latitude":526,"longitude":527,"openning_date":528,"openning_type":529,"covered_grades":532,"school_type":559,"ownership_type":560,"class_date":562,"pre_open_reception_flg":464,"citation":563},345058,16,"2026-03-22T22:36:10+09:00","2026-06-29T14:09:19+09:00",8,14012,"基本情報","https:\u002F\u002Faxis-kobetsu.jp\u002Fschools\u002Fpreview\u002Fid\u002F0","[校舎] 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