{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b2c494fa-bf65-450e-99b8-07c997b1d846",
   "metadata": {},
   "source": [
    "## The TetraBook and S3\n",
    "\n",
    "A Jupyter Notebook for the School of Tomorrow.\n",
    "\n",
    "With thanks to Alan Michelson on Synergeo, for circling back to it, and to David Koski, for the TetraBook meme in the first place.\n",
    "\n",
    "[View in nbviewer](https://nbviewer.org/github/4dsolutions/School_of_Tomorrow/blob/master/TetraBook.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "fda9e374-30aa-4ce0-a2ca-12724db39940",
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import YouTubeVideo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1960684d-cb7e-4a90-b462-7fab4ed09f8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/WKrGmuXW-RQ\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1125e8790>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo(\"WKrGmuXW-RQ\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "71f41d58-cca6-4994-bc7a-822b4322e808",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4c392a18-9d2b-4f16-96d3-2fdd88a712be",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bef4b5c4-bf9d-409b-a403-636f20252999",
   "metadata": {},
   "outputs": [],
   "source": [
    "root3 = math.sqrt(3)\n",
    "S3 = math.sqrt(9/8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "559103cb-46af-4114-b476-d4d86ab7f859",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.4641016151377544"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * root3 # book cover tip to book cover tip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0c752872-11a9-46b5-a2ff-9e616e065ca1",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_deg = np.arange(0, 181) # degrees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3efad524-6e9b-4828-b206-f77d996ce174",
   "metadata": {},
   "outputs": [],
   "source": [
    "front_cover_tip = (-root3, 0.0)  # left\n",
    "back_cover_tip  = ( root3, 0.0)  # right"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5dc80f09-4d97-4612-a56d-d9a82355fab7",
   "metadata": {},
   "outputs": [],
   "source": [
    "page_tip_deg = lambda deg: (-root3 * np.cos(np.radians(deg)), root3 * (np.sin(np.radians(deg))))\n",
    "page_tip_rad = lambda rad: (-root3 * np.cos(rad), root3 * np.sin(rad))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9f3a2f62-1885-4bc3-ba25-d452efd0c8c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.0605752387249068e-16, 1.7320508075688772)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "page_tip_rad(math.pi/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d3450655-e0c8-470d-a08d-618465e4073b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "70.52877936550931"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dihedral_angle_of_reg_tet = math.acos(1/3)\n",
    "math.degrees(dihedral_angle_of_reg_tet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "985838f7-0366-4ff7-86ab-49535aa7998d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def distance(a, b):\n",
    "    return np.sqrt((a[0] - b[0])**2 + (a[1] - b[1])**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "bfaa4d07-0a3a-4d9f-b536-e1ad1f0872dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.4641016151377544"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance(front_cover_tip, back_cover_tip)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "05dabb6f-aa23-44d8-9405-0b1e6255c003",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.449489742783178"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance(front_cover_tip, page_tip_deg(90))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "534c901e-dcd0-4eaf-9f88-3654246cb0e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.4641016151377544"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distance(front_cover_tip, page_tip_deg(180))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2a00560-9a3c-4c79-87f2-d53d8d5fa6b4",
   "metadata": {},
   "source": [
    "<a data-flickr-embed=\"true\" href=\"https://www.flickr.com/photos/kirbyurner/46149255411/in/photolist-2ncC3Xn-2mZypyZ-2dj3ZQP-2dj3ZPr-Sb76Cn-S6Quyu-S6QuFd\" title=\"tetrabook2\"><img src=\"https://live.staticflickr.com/4850/46149255411_31eb8869cf.jpg\" width=\"500\" height=\"341\" alt=\"tetrabook2\"></a><script async src=\"//embedr.flickr.com/assets/client-code.js\" charset=\"utf-8\"></script>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "d686c0f1-e3bc-4d87-bf1e-13d909163ab5",
   "metadata": {},
   "outputs": [],
   "source": [
    "import imp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b75c66a0-511a-4371-8da6-5cef878f57a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'tetravolume' from '/Users/kirbyurner/Documents/School_of_Tomorrow/tetravolume.py'>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import tetravolume\n",
    "imp.reload(tetravolume)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "a4cb182d-560c-4afc-8600-79cd9bd596ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "import tetravolume as tv\n",
    "from tetravolume import Tetrahedron"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1d4a6a24-5b74-4422-abcb-1c1caffb071d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tv.D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ed4c62a1-5cb5-4746-9054-2a229744538e",
   "metadata": {},
   "outputs": [],
   "source": [
    "test_tet = Tetrahedron(1,1,1,1,1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "5254f86b-22dc-4c22-9613-1e018e15961f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_tet.ivm_volume()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "cc0e7a45-ef5c-4c8f-a32e-bf820abe1bcd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_volume_rad(theta):\n",
    "    return Tetrahedron(1,1,1,1,1, distance(back_cover_tip, page_tip_rad(theta))/2).ivm_volume()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d399e4ab-47ab-44ac-957b-581d592ff40e",
   "metadata": {},
   "outputs": [],
   "source": [
    "get_vol = np.vectorize(get_volume_rad)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "a62b6789-169a-44ac-bdc8-67adbe76ba33",
   "metadata": {},
   "outputs": [],
   "source": [
    "table = pd.DataFrame({\"theta_deg\":theta_deg, \"theta_rad\":np.radians(theta_deg)})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b8172027-099e-4b42-adf3-f38aa95c4ec8",
   "metadata": {},
   "outputs": [
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       "   theta_deg  theta_rad\n",
       "0          0   0.000000\n",
       "1          1   0.017453\n",
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       "3          3   0.052360\n",
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   "outputs": [],
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    "table[\"alt\"] = table.theta_rad.apply(lambda r: root3 * math.sin(r))\n",
    "table[\"tvs\"] = table.theta_rad.apply(get_volume_rad)\n",
    "table[\"x\"]   = table.theta_rad.apply(lambda r: root3 * math.cos(r))"
   ]
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   "execution_count": 27,
   "id": "55af267b-4fef-46c5-9bf3-bbaea4d7bb86",
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       "     theta_deg  theta_rad           alt           tvs         x\n",
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       "..         ...        ...           ...           ...       ...\n",
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       "180        180   3.141593  2.121150e-16  0.000000e+00 -1.732051\n",
       "\n",
       "[181 rows x 5 columns]"
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     "execution_count": 27,
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   "execution_count": 28,
   "id": "91c6023b-78e7-44cf-a278-3e11e2e9e7a2",
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       "     theta_deg  theta_rad         x           alt           tvs\n",
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       "\n",
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     "execution_count": 28,
     "metadata": {},
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    "table = table.reindex(columns=[\"theta_deg\", \"theta_rad\", \"x\", \"alt\", \"tvs\"])\n",
    "table"
   ]
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  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6389e390-008a-4e4e-9f56-6842ed6f7355",
   "metadata": {},
   "outputs": [
    {
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       "   theta_deg  theta_rad     x   alt   tvs\n",
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    "pd.reset_option(\"display.precision\", 5)\n",
    "pd.set_option(\"display.float_format\", \"{:.3f}\".format)\n",
    "table.head()"
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  {
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   "execution_count": 30,
   "id": "0b748a07-c4cc-4fd0-a9c3-a64d70c67cd9",
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   "outputs": [
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       "      <td>3</td>\n",
       "      <td>0.052</td>\n",
       "      <td>1.730</td>\n",
       "      <td>0.091</td>\n",
       "      <td>0.056</td>\n",
       "      <td>0.052</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>0.070</td>\n",
       "      <td>1.728</td>\n",
       "      <td>0.121</td>\n",
       "      <td>0.074</td>\n",
       "      <td>0.070</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   theta_deg  theta_rad     x   alt   tvs   cus\n",
       "0          0      0.000 1.732 0.000 0.000 0.000\n",
       "1          1      0.017 1.732 0.030 0.019 0.017\n",
       "2          2      0.035 1.731 0.060 0.037 0.035\n",
       "3          3      0.052 1.730 0.091 0.056 0.052\n",
       "4          4      0.070 1.728 0.121 0.074 0.070"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table[\"cus\"] = table.tvs.apply(lambda c: c/S3)\n",
    "table.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "0b2bd53b-d853-443f-af87-9e465fb650e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "b9303225-aee4-49e9-8dc6-80afc4ff7302",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(10,10))\n",
    "\n",
    "ax.plot('theta_rad', 'tvs', data=table, label=\"Tetravols\")\n",
    "ax.plot('theta_rad', 'alt', data=table, label=\"Altitude\")\n",
    "\n",
    "# ax.set_box_aspect(1)\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "ax.set_xlim(0,3.5)\n",
    "ax.set_xticks(np.arange(0, 3.5, 0.2))\n",
    "ax.set_xlabel(\"Theta (radians)\")\n",
    "\n",
    "ax.set_ylim(0,2.0)\n",
    "ax.set_yticks(np.arange(0, 2.0, 0.2))\n",
    "ax.set_ylabel(\"TVs / Page Altitude\")\n",
    "ax.set_title(\"Theta versus Tetravolumes\")\n",
    "\n",
    "ax.grid()\n",
    "\n",
    "ax.axhline(1.06066, color='green', ls=\"-\", dashes = (5, 2, 1, 2), label=\"S3\")\n",
    "ax.axvline(math.acos(1/3), color='blue', dashes = (5, 2), label=\"Reg Tet\")\n",
    "ax.axvline(math.acos(-1/3), color='blue', dashes = (5, 2))\n",
    "\n",
    "ax.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "fc246c6c-8ac6-440a-98ed-f41a0fa128cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(10,10))\n",
    "\n",
    "ax.plot('x', 'tvs', data=table, label=\"Tetravols\")\n",
    "ax.plot('x', 'alt', data=table, label=\"Page Tip\")\n",
    "\n",
    "# ax.set_box_aspect(1)\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "ax.set_xlim(-2,2)\n",
    "ax.set_xticks(np.arange(-2, 2, 0.2))\n",
    "ax.set_xlabel(\"X coord\", fontsize=12)\n",
    "\n",
    "ax.yaxis.set_label_position(\"left\")\n",
    "ax.set_ylabel(\"Page Altitude (Y coord)\\nTetravolumes\", fontsize=12)\n",
    "ax.set_title(\"TetraBook Page Sweepout\")\n",
    "\n",
    "ax.set_ylim(0,2)\n",
    "ax.set_yticks(np.arange(0, 2.0, 0.2))\n",
    "\n",
    "ax.grid()\n",
    "\n",
    "ax.axhline(1.06066, color='green', ls=\"-\", dashes = (5, 2, 1, 2), label=\"S3\")\n",
    "ax.axvline(root3 * math.cos(math.acos( 1/3)), color='blue', dashes = (5, 2), label=\"Reg Tet\")\n",
    "ax.axvline(root3 * math.cos(math.acos(-1/3)), color='blue', dashes = (5, 2))\n",
    "\n",
    "ax.legend()\n",
    "\n",
    "plt.savefig(\"tetrabook_plot.png\", format=\"png\", bbox_inches=\"tight\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "ec3aa56d-36c6-4473-b1e6-522ee1f7e162",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(10,10))\n",
    "\n",
    "ax.plot('x', 'cus', data=table, label=\"Cubes (R)\")\n",
    "ax.plot('x', 'alt', data=table, label=\"Page Tip\")\n",
    "\n",
    "# ax.set_box_aspect(1)\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "ax.set_xlim(-2,2)\n",
    "ax.set_xticks(np.arange(-2, 2, 0.2))\n",
    "ax.set_xlabel(\"X coord\", fontsize=12)\n",
    "\n",
    "ax.yaxis.set_label_position(\"left\")\n",
    "ax.set_ylabel(\"Page Altitude (Y coord)\\nCube Volumes\", fontsize=12)\n",
    "ax.set_title(\"TetraBook Page Sweepout\")\n",
    "\n",
    "ax.set_ylim(0,2)\n",
    "ax.set_yticks(np.arange(0, 2.0, 0.2))\n",
    "\n",
    "ax.grid()\n",
    "\n",
    "ax.axhline(1/S3, color='green', ls=\"-\", dashes = (5, 2, 1, 2), label=\"1/S3\")\n",
    "ax.axvline(root3 * math.cos(math.acos( 1/3)), color='blue', dashes = (5, 2), label=\"Reg Tet\")\n",
    "ax.axvline(root3 * math.cos(math.acos(-1/3)), color='blue', dashes = (5, 2))\n",
    "\n",
    "ax.legend()\n",
    "\n",
    "plt.savefig(\"tetrabook_cu_plot.png\", format=\"png\", bbox_inches=\"tight\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b9e8a6c-bb79-4ff9-81aa-7b9b41b93f4b",
   "metadata": {},
   "source": [
    "## Recap \n",
    "<a data-flickr-embed=\"true\" href=\"https://www.flickr.com/photos/kirbyurner/9533679790/in/album-72157624750749042/\" title=\"Triangular Book with One Page\"><img src=\"https://live.staticflickr.com/7450/9533679790_b916fba31f_w.jpg\" width=\"400\" height=\"300\" alt=\"Triangular Book with One Page\"></a><script async src=\"//embedr.flickr.com/assets/client-code.js\" charset=\"utf-8\"></script>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "0b495c15-ada0-4443-bf09-63a0b64e24f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import sqrt as rt2\n",
    "import sympy as sym\n",
    "from sympy import Eq, Number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "b60652d9-6926-490c-969a-d2252fe58cd4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{3}}{2}$"
      ],
      "text/plain": [
       "sqrt(3)/2"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "book_edge = sym.symbols([\"book_edge\", \"altitude\"])\n",
    "book_edge = Number(1)\n",
    "altitude = sym.sqrt(book_edge**2 - (book_edge/2)**2)\n",
    "altitude"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "db98984d-0f4f-4a5a-bb9f-e16f11465412",
   "metadata": {},
   "outputs": [],
   "source": [
    "right_tet_hyp = sym.sqrt(2 * altitude**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "23135026-13e1-4f93-9a75-5a9f03c42a51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{6}}{2}$"
      ],
      "text/plain": [
       "sqrt(6)/2"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "right_tet_hyp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "2fc89b32-a87e-4a85-af28-6f3a85c1da8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "tv = Tetrahedron(1,1,1,1,1,right_tet_hyp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "c084204f-443b-496e-b3ec-d6817cafcd94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tv.xyz_volume()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "e0b27fed-6c59-461b-b8ad-5ab91dab62ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{3 \\sqrt{2}}{4}$"
      ],
      "text/plain": [
       "3*sqrt(2)/4"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tv.ivm_volume()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}