.. -*- coding: utf-8 -*-

========================================
 Solid Pentominoes: Puzzles & Solutions
========================================

:Author: David Goodger <goodger@python.org>
:Date: $Date: 2017-01-15 12:38:21 -0600 (Sun, 15 Jan 2017) $
:Revision: $Revision: 648 $
:Web site: http://puzzler.sourceforge.net/
:Copyright: |c| 1998-2016 by David J. Goodger
:License: `GPL 2 <../COPYING.html>`__

.. image:: images/puzzler.png
   :align: center

.. sidebar:: Also see:

   * `Polycubes: Puzzles & Solutions <polycubes.html>`_
   * `Pentacubes: Puzzles & Solutions <pentacubes.html>`_
   * `Pentominoes: Puzzles & Solutions <pentominoes.html>`_
   * `Polyominoes: Puzzles & Solutions <polyominoes.html>`_
   * `An Introduction to Polycubes <polycubes-intro.html>`_
   * `Notes on Polycubes <polycube-notes.html>`_
   * `An Introduction to Polyominoes <polyominoes-intro.html>`_
   * `Notes on Polyominoes <polyomino-notes.html>`_
   * `Polyform Puzzler: Puzzles & Solutions <puzzles.html>`_
   * `Polyform Puzzler FAQ <FAQ.html>`_
     (`polyform details <FAQ.html#what-polyforms-are-there>`__,
     `numbers of polyforms <FAQ.html#how-many-of-each-type-of-polyform-are-there>`__,
     `interpreting solution files <FAQ.html#how-should-polycube-solution-files-be-interpreted>`__)

.. contents::


Solids
======

* 2x3x10: `12 solutions
  <../solutions/cubes/solid-pentominoes-2x3x10.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-2x3x10.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-2x3x10.png

* 2x5x6: `264 solutions
  <../solutions/cubes/solid-pentominoes-2x5x6.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-2x5x6.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-2x5x6.png

* 3x4x5: `3940 solutions
  <../solutions/cubes/solid-pentominoes-3x4x5.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-3x4x5.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-3x4x5.png


Ring Walls
==========

(rectangular walls, 1 cube thick, with hollow centers):

* 3x3x9: `3 solutions
  <../solutions/cubes/solid-pentominoes-3x3x9-ring.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-3x3x9-ring.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-3x3x9-ring.png

* 3x5x7: `1 solution
  <../solutions/cubes/solid-pentominoes-3x5x7-ring.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-3x5x7-ring.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-3x5x7-ring.png

* 5x3x5: `186 solutions
  <../solutions/cubes/solid-pentominoes-5x3x5-ring.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-5x3x5-ring.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-5x3x5-ring.png

* 6x3x4: `46 solutions
  <../solutions/cubes/solid-pentominoes-6x3x4-ring.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-6x3x4-ring.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-6x3x4-ring.png

Three other rings with no solutions were also implemented: 3x4x8,
3x6x6, and 5x4x4.


Open Boxes
==========

* 8x3x3: `solutions incomplete
  <../solutions/cubes/solid-pentominoes-open-box-8x3x3.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-open-box-8x3x3.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-open-box-8x3x3.png

* 6x3x4: `solutions incomplete
  <../solutions/cubes/solid-pentominoes-open-box-6x3x4.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-open-box-6x3x4.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-open-box-6x3x4.png


Steps
=====

* 5x5x4: `137 solutions
  <../solutions/cubes/solid-pentominoes-5x5x4-steps.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-5x5x4-steps.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-5x5x4-steps.png

* 4x4x6: `279 solutions
  <../solutions/cubes/solid-pentominoes-4x4x6-steps.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-4x4x6-steps.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-4x4x6-steps.png

* 3x3x10: `9 solutions
  <../solutions/cubes/solid-pentominoes-3x3x10-steps.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-3x3x10-steps.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-3x3x10-steps.png


Crystals
========

* 4x4x8: `251 solutions
  <../solutions/cubes/solid-pentominoes-4x4x8-crystal.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-4x4x8-crystal.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-4x4x8-crystal.png

* 6x6x6:

  .. list-table::
     :class: borderless

     * - .. figure:: images/cubes/solid-pentominoes-6x6x6-crystal-1.png

            `2 solutions
            <../solutions/cubes/solid-pentominoes-6x6x6-crystal-1.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-6x6x6-crystal-1.x3d>`__)

       - .. figure:: images/cubes/solid-pentominoes-6x6x6-crystal-2.png

            `1 solution
            <../solutions/cubes/solid-pentominoes-6x6x6-crystal-2.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-6x6x6-crystal-2.x3d>`__)

       - .. figure:: images/cubes/solid-pentominoes-6x6x6-crystal-3.png

            `9 solutions
            <../solutions/cubes/solid-pentominoes-6x6x6-crystal-3.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-6x6x6-crystal-3.x3d>`__)

     * - .. figure:: images/cubes/solid-pentominoes-6x6x6-crystal-4.png

            `2 solutions
            <../solutions/cubes/solid-pentominoes-6x6x6-crystal-4.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-6x6x6-crystal-4.x3d>`__)

       - .. figure:: images/cubes/solid-pentominoes-6x6x6-crystal-5.png

            `4 solutions
            <../solutions/cubes/solid-pentominoes-6x6x6-crystal-5.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-6x6x6-crystal-5.x3d>`__)

       -


Misc
====

* 3x5x7 slope: `116 solutions
  <../solutions/cubes/solid-pentominoes-3x5x7-slope.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-3x5x7-slope.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-3x5x7-slope.png

* Towers:

  .. list-table::
     :class: borderless

     * - .. figure:: images/cubes/solid-pentominoes-tower-1.png

            `27 solutions
            <../solutions/cubes/solid-pentominoes-tower-1.txt>`__
            (core hollow; design by David Klarner; `X3D model
            <images/cubes/solid-pentominoes-tower-1.x3d>`__)

       - .. figure:: images/cubes/solid-pentominoes-tower-2.png

            `10 solution
            <../solutions/cubes/solid-pentominoes-tower-2.txt>`__
            (core hollow; design by David Klarner; `X3D model
            <images/cubes/solid-pentominoes-tower-2.x3d>`__)

       - .. figure:: images/cubes/solid-pentominoes-tower-3.png

            `many solutions
            <../solutions/cubes/solid-pentominoes-tower-3.txt>`__
            (design by Leslie Young, via `Kadon's Quintillions`_
            booklet; ; `X3D model
            <images/cubes/solid-pentominoes-tower-3.x3d>`__)

* Ohno's block (design by Yoshio Ohno, via `Kadon's Quintillions`_
  booklet, titled "A Gift From Japan"): `1 solution
  <../solutions/cubes/solid-pentominoes-ohnos-block.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-ohnos-block.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-ohnos-block.png

* Spinner block: `42 solutions
  <../solutions/cubes/solid-pentominoes-spinner-block.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-spinner-block.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-spinner-block.png

* Corner walls (the far corner cube is empty): `253 solutions
  <../solutions/cubes/solid-pentominoes-corner-walls.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-corner-walls.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-corner-walls.png

* Corner piece (design from `Kadon's Quintillions`_ booklet): `70
  solutions <../solutions/cubes/solid-pentominoes-corner-piece.txt>`__ (`X3D
  model <images/cubes/solid-pentominoes-corner-piece.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-corner-piece.png

* Three walls (design from `Kadon's Quintillions`_ booklet): `90
  solutions <../solutions/cubes/solid-pentominoes-three-walls.txt>`__ (`X3D
  model <images/cubes/solid-pentominoes-three-walls.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-three-walls.png

* Empty bottle (hollow central 1x1x5; design from `Kadon's
  Quintillions`_ booklet): `49 solutions
  <../solutions/cubes/solid-pentominoes-empty-bottle.txt>`__ (`X3D model
  <images/cubes/solid-pentominoes-empty-bottle.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-empty-bottle.png

* Condominium B (design from `Kadon's Quintillions`_ booklet): `1
  solution <../solutions/cubes/solid-pentominoes-condominium-b.txt>`__ (`X3D
  model <images/cubes/solid-pentominoes-condominium-b.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-condominium-b.png

* Cross blocks:

  .. list-table::
     :class: borderless

     * - .. figure:: images/cubes/solid-pentominoes-cross-block-1.png

            `92 solutions
            <../solutions/cubes/solid-pentominoes-cross-block-1.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-cross-block-1.x3d>`__)
  
       - .. figure:: images/cubes/solid-pentominoes-cross-block-2.png

            `15 solutions
            <../solutions/cubes/solid-pentominoes-cross-block-2.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-cross-block-2.x3d>`__)

     * - .. figure:: images/cubes/solid-pentominoes-cross-block-3.png

            `10 solutions
            <../solutions/cubes/solid-pentominoes-cross-block-3.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-cross-block-3.x3d>`__)

       -

* Quarter Pyramid: a 55-cube shape, so 11 pieces are used and one
  piece must be omitted.  `320 solutions
  <../solutions/cubes/solid-pentominoes-5x5x5-quarter-pyramid.txt>`__
  (`X3D model
  <images/cubes/solid-pentominoes-5x5x5-quarter-pyramid.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-5x5x5-quarter-pyramid.png

  Solutions omitting F: 11; I: 7; L: none; N: 4; P: none; T: 22; U: 4;
  V: 12; W: 10; X: 223; Y: 2; Z: 25.

* Cross Tower (design from `Thimo Rosenkranz's pentoma.de
  <http://www.pentoma.de>`_): `7 solutions
  <../solutions/cubes/solid-pentominoes-cross-tower.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-cross-tower.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-cross-tower.png

* Infinity Tower (design from `Thimo Rosenkranz's pentoma.de`_): `1 solution
  <../solutions/cubes/solid-pentominoes-infinity-tower.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-infinity-tower.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-infinity-tower.png

* Square Towers:

  .. list-table::
     :class: borderless

     * - .. figure:: images/cubes/solid-pentominoes-square-tower-1.png

            `1 solution
            <../solutions/cubes/solid-pentominoes-square-tower-1.txt>`__
            (design from `Thimo Rosenkranz's pentoma.de`_; `X3D model
            <images/cubes/solid-pentominoes-square-tower-1.x3d>`__)

       - .. figure:: images/cubes/solid-pentominoes-square-tower-2.png

            `54 solutions
            <../solutions/cubes/solid-pentominoes-square-tower-2.txt>`__
            (design from `Thimo Rosenkranz's pentoma.de`_; `X3D model
            <images/cubes/solid-pentominoes-square-tower-2.x3d>`__)

     * - .. figure:: images/cubes/solid-pentominoes-square-tower-3.png

            `27 solutions
            <../solutions/cubes/solid-pentominoes-square-tower-3.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-square-tower-3.x3d>`__)

       - .. figure:: images/cubes/solid-pentominoes-square-tower-4.png

            `8 solutions
            <../solutions/cubes/solid-pentominoes-square-tower-4.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-square-tower-4.x3d>`__)

     * - .. figure:: images/cubes/solid-pentominoes-square-tower-5.png

            `106 solutions
            <../solutions/cubes/solid-pentominoes-square-tower-5.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-square-tower-5.x3d>`__)

       - .. figure:: images/cubes/solid-pentominoes-square-tower-6.png

            `154 solutions
            <../solutions/cubes/solid-pentominoes-square-tower-6.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-square-tower-6.x3d>`__)

* Stairstep walls:

  .. list-table::
     :class: borderless

     * - .. figure:: images/cubes/solid-pentominoes-stairstep-walls-1.png

            `34 solutions
            <../solutions/cubes/solid-pentominoes-stairstep-walls-1.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-stairstep-walls-1.x3d>`__)

       - .. figure:: images/cubes/solid-pentominoes-stairstep-walls-2.png

            `1 solution
            <../solutions/cubes/solid-pentominoes-stairstep-walls-2.txt>`__
            (`X3D model
            <images/cubes/solid-pentominoes-stairstep-walls-2.x3d>`__)

* Stepped pyramid (design suggested by Colin Lacy): `55 solutions
  <../solutions/cubes/solid-pentominoes-5x5x4-stepped-pyramid.txt>`__
  (`X3D model <images/cubes/solid-pentominoes-5x5x4-stepped-pyramid.x3d>`__)

  .. image:: images/cubes/solid-pentominoes-5x5x4-stepped-pyramid.png

.. _Kadon's Quintillions: http://gamepuzzles.com/polycube.htm#Q

.. |c| unicode:: U+00A9 .. copyright sign