Difference between revisions of "Interior template"

From HexWiki
Jump to: navigation, search
(Fixed diagram syntax.)
(mouth -> trapezoid)
 
(9 intermediate revisions by the same user not shown)
Line 1: Line 1:
This page lists some interior templates. In each case, the carrier of the template is indicated by cells marked "*".
+
This page lists some interior templates. In each case, the carrier of the template consists of the cells that are shown in its diagram.
  
 
== 2- and 3-stone templates ==
 
== 2- and 3-stone templates ==
Line 6: Line 6:
 
<hexboard size="3x2"
 
<hexboard size="3x2"
 
   coords="hide"
 
   coords="hide"
   contents="R a3 R b1 E *:a2 E *:b2"
+
  edges="none"
 +
  visible="area(b1,a2,a3,b2)"
 +
   contents="R a3 R b1"
 
   />
 
   />
  
 
=== The wheel ===
 
=== The wheel ===
 +
 
<hexboard size="3x3"
 
<hexboard size="3x3"
 
   coords="hide"
 
   coords="hide"
   contents="R a3 R b1 R c2 E *:a2 E *:b2 E *:b3 E *:c1"
+
  edges="none"
 +
  visible="-a1 c3"
 +
   contents="R a3 R b1 R c2"
 
   />
 
   />
  
Line 19: Line 24:
 
These templates are grouped by the size and shape of their carrier.
 
These templates are grouped by the size and shape of their carrier.
  
=== The mouth or trapezoid ===
+
=== The trapezoid ===
 +
 
 
<hexboard size="3x3"
 
<hexboard size="3x3"
 
   coords="hide"
 
   coords="hide"
   contents="R a3 R b1 R c1 R c3 E *:a2 *:b2 *:b3 *:c2"
+
  edges="none"
 +
  visible="-c3"
 +
   contents="R a1 a3 b3 c1"
 
   />
 
   />
  
 
=== The crescent ===
 
=== The crescent ===
 +
 
<hexboard size="3x3"
 
<hexboard size="3x3"
 
   coords="hide"
 
   coords="hide"
   contents="R a3 R b1 R a2 R c3 E *:c1 *:b2 *:b3 *:c2"
+
  edges="none"
 +
  visible="-c3"
 +
   contents="R a1 a3 b3 c2"
 
   />
 
   />
  
 
=== The span ===
 
=== The span ===
 +
 
<hexboard size="3x4"
 
<hexboard size="3x4"
 
   coords="hide"
 
   coords="hide"
   contents="R a2 R a3 R c3 R d2 E *:b1 *:b2 *:b3 *:c1 *:c2 *:d1"
+
  edges="none"
 +
  visible="-a1 d3"
 +
   contents="R a2 R a3 R c3 R d2"
 
   />
 
   />
  
 
=== The parallelogram ===
 
=== The parallelogram ===
 +
 
<hexboard size="3x4"
 
<hexboard size="3x4"
 
   coords="hide"
 
   coords="hide"
   contents="R a2 R a3 R d1 R d2 E *:b1 *:b2 *:b3 *:c1 *:c2 *:c3"
+
  edges="none"
 +
  visible="-a1 d3"
 +
   contents="R a2 R a3 R d1 R d2"
 
   />
 
   />
  
 
=== The box ===
 
=== The box ===
 +
 
<hexboard size="3x4"
 
<hexboard size="3x4"
 
   coords="hide"
 
   coords="hide"
   contents="R b1 R a3 R c3 R d1 E *:a2 *:b2 *:b3 *:c1 *:c2 *:d2"
+
  edges="none"
 +
  visible="-a1 d3"
 +
   contents="R b1 R a3 R c3 R d1"
 
   />
 
   />
  
 
=== The diamond ===
 
=== The diamond ===
 +
 
<hexboard size="3x4"
 
<hexboard size="3x4"
 
   coords="hide"
 
   coords="hide"
   contents="R a2 R c1 R b3 R d2 E *:b1 *:b2 *:c3 *:a3 *:c2 *:d1"
+
  edges="none"
 +
  visible="-a1 d3"
 +
   contents="R a2 R c1 R b3 R d2"
 
   />
 
   />
  
=== Unnamed templates ===
+
=== The shopping cart ===
 +
[[Image: ShoppingCart.png|right|150px]]
  
The following templates have not yet been named.
 
 
'''Proposed name: The open box'''
 
 
This template has the same carrier as the box, and differs from it only in that the "lid" of the box is open.
 
 
<hexboard size="3x4"
 
<hexboard size="3x4"
 
   coords="hide"
 
   coords="hide"
   contents="R b1 R a3 R d1 R d2 E *:a2 *:b2 *:b3 *:c1 *:c2 *:c3"
+
  edges="none"
 +
  visible="-a1 d3"
 +
   contents="R b1 R a3 R c3 R d2"
 
   />
 
   />
  
'''Proposed name: The scooter''' [[Image: Scooter.png|right|150px]]
+
=== The scooter ===
 +
[[Image: Scooter.png|right|150px]]
 +
 
 
<hexboard size="4x4"
 
<hexboard size="4x4"
 
   coords="hide"
 
   coords="hide"
   contents="R b2 R a4 R c1 R c4 E *:a3 *:b3 *:b4 *:c2 *:c3 *:d1 *:d2 *:d3"
+
  edges="none"
 +
  visible="area(c1,a3,a4,c4,d3,d1)"
 +
   contents="R b2 R a4 R c1 R c4"
 
   />
 
   />
  
'''Proposed name: The bicycle''' [[Image: Bicycle.png|right|150px]]
+
=== The bicycle ===
 +
[[Image: Bicycle.png|right|150px]]
 +
 
 
<hexboard size="4x4"
 
<hexboard size="4x4"
 
   coords="hide"
 
   coords="hide"
   contents="R b2 R a4 R d1 R c4 E *:a3 *:b3 *:b4 *:c1 *:c2 *:c3 *:d2 *:d3"
+
  edges="none"
 +
  visible="area(c1,a3,a4,c4,d3,d1)"
 +
   contents="R b2 R a4 R d1 R c4"
 
   />
 
   />
  
'''Proposed name: The hammock''' [[Image: Hammock.png|right|150px]]  
+
=== The hammock ===
 +
[[Image: Hammock.png|right|150px]]  
 +
 
 +
This template is a variation of the diamond that only guarantees a connection between the two stones marked with arrows. It does not guarantee all 4 stones to be connected.
  
This template is a variation of the diamond that only guarantees a connection between the two stones marked "1". It does not guarantee all 4 stones to be connected.
 
 
<hexboard size="3x4"
 
<hexboard size="3x4"
 
   coords="hide"
 
   coords="hide"
   contents="R 1:a1 R c1 R b3 R 1:d2 E *:a2 *:b1 *:b2 *:c3 *:a3 *:c2 *:d1"
+
  edges="none"
 +
  visible="-d3"
 +
   contents="R arrow(10):a1 R c1 R b3 R arrow(4):d2"
 
   />
 
   />
  
'''Proposed name: The long parallelogram'''
+
=== The wide parallelogram ===
 +
 
 
<hexboard size="4x4"
 
<hexboard size="4x4"
 
   coords="hide"
 
   coords="hide"
   contents="R a2 R a3 R d2 R d3 E *:a4 *:b1 *:b2 *:b3 *:b4 *:c1 *:c2 *:c3 *:c4 *:d1"
+
  edges="none"
 +
  visible="-a1 d4"
 +
   contents="R a2 R a3 R d2 R d3"
 +
  />
 +
 
 +
== Long version of templates ==
 +
 
 +
Several interior templates have "long" versions. These work at any length, and are basically [[#Interior templates from edge templates|interior versions]] of second row ladder escapes.
 +
 
 +
=== The long crescent ===
 +
 
 +
<hexboard size="3x6"
 +
  coords="hide"
 +
  edges="none"
 +
  visible="-f3"
 +
  contents="R a1 a3 b3 c3 d3 e3 f2"
 +
  />
 +
 
 +
=== The long trapezoid ===
 +
 
 +
There are several ways of making a long trapezoid. Two of them are shown here:
 +
 
 +
<hexboard size="3x6"
 +
  coords="hide"
 +
  edges="none"
 +
  visible="-f3"
 +
  contents="R a1 a3 b3 c3 d3 e3 f1"
 +
  />
 +
<hexboard size="3x6"
 +
  coords="hide"
 +
  edges="none"
 +
  visible="-f3"
 +
  contents="R a1 a3 b3 c3 d3 f1 f2"
 +
  />
 +
 
 +
=== The long span ===
 +
 
 +
<hexboard size="3x6"
 +
  coords="hide"
 +
  edges="none"
 +
  visible="-a1 f3"
 +
  contents="R a2 a3 c3 d3 e3 f2"
 +
  />
 +
 
 +
The long span is relatively common as an edge template. The most common example of this is [[Fifth_row_edge_templates#V-2-k|edge template V2-k]]:
 +
<hexboard size="5x4"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="-a1--a4 b1"
 +
  contents="R b2 b4 c1 E a:a5 b:b5 S red:(a5 b5)"
 +
  />
 +
Note that the cells marked "a" and "b", which belong to the carrier of this template, are [[captured cell|captured]] by Red, and therefore this really is an edge version of the long span. For the same reason, the following is an edge template as well:
 +
<hexboard size="6x4"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="-a1--a5 b1"
 +
  contents="R b2 b4 b5 c1"
 
   />
 
   />
  
 
== Template extensions ==
 
== Template extensions ==
  
Given a template, it is often possible to '''extend''' the template by adding one or more stones that threatens to connect to the template in two different ways. For example, the following 5-stone templates are extensions of the trapezoid:
+
Given a template, it is often possible to '''extend''' the template by adding one or more stones that threaten to connect to the template in two different ways. For example, the following 5-stone templates are extensions of the trapezoid. In each case, the trapezoid is shown in white and the extension in gray.
 
<hexboard size="3x5"
 
<hexboard size="3x5"
 
   coords="hide"
 
   coords="hide"
   contents="R a3 b1 c1 c3 e1 E *:a2 *:b2 *:b3 *:c2 *:d1 *:d2"
+
  edges="none"
 +
  visible="-a1 d3 e2 e3"
 +
   contents="R a3 b1 c1 c3 e1 S gray:(d1,d2,e1)"
 
   />
 
   />
 
<hexboard size="4x6"
 
<hexboard size="4x6"
 
   coords="hide"
 
   coords="hide"
   contents="R a4 b2 c2 c4 f2 E *:a3 *:b3 *:b4 *:c3 *:d2 *:d3 *:d1 *:e1 *:e2 *:f1 *:e3 *:d4"
+
  edges="none"
 +
  visible="-a1--c1 a2 e4 f3 f4"
 +
   contents="R a4 b2 c2 c4 f2 S gray:area(d1,d4,f2,f1)"
 
   />
 
   />
 
Because template extensions are so numerous, they usually do not get their own names, and it is not usually worth memorizing them as separate templates.
 
Because template extensions are so numerous, they usually do not get their own names, and it is not usually worth memorizing them as separate templates.
Line 111: Line 205:
 
<hexboard size="4x4"
 
<hexboard size="4x4"
 
   coords="hide"
 
   coords="hide"
   contents="R c1 a4 b4 c4 E *:a3 *:b2 *:b3 *:c2 *:c3 *:d1 *:d2 *:d3"
+
  edges="none"
 +
  visible="area(c1,a3,a4,c4,d3,d1)"
 +
   contents="R c1 a4 b4 c4 S area(c1,a3,d3,d1)"
 
   />
 
   />
 
To simulate an edge, it is not actually necessary to have a solid row of stones; it is sufficient that each cell on "row 1" of the edge is adjacent to a connected red stone. For example, the following is another variant of an interior ziggurat:
 
To simulate an edge, it is not actually necessary to have a solid row of stones; it is sufficient that each cell on "row 1" of the edge is adjacent to a connected red stone. For example, the following is another variant of an interior ziggurat:
 
<hexboard size="5x4"
 
<hexboard size="5x4"
 
   coords="hide"
 
   coords="hide"
   contents="R c1 a4 b5 c4 E *:a3 *:b2 *:b3 *:c2 *:c3 *:d1 *:d2 *:d3 *:a5 *:b4"
+
  edges="none"
 +
  visible="area(c1,a3,a5,b5,d3,d1)"
 +
   contents="R c1 a4 b5 c4 S area(c1,a3,d3,d1)"
 
   />
 
   />
 
One can construct a virtually unlimited number of templates this way. Here is an example of an interior [[Edge template IV2a|IV-2-a]] attached to a [[trapezoid]]:
 
One can construct a virtually unlimited number of templates this way. Here is an example of an interior [[Edge template IV2a|IV-2-a]] attached to a [[trapezoid]]:
 
<hexboard size="7x5"
 
<hexboard size="7x5"
 
   coords="hide"
 
   coords="hide"
   contents="R d1 e1 a5 c5 a7 c6 E *:a4 *:a6 *:b3 *:b4 *:b5 *:b6 *:b7 *:c2 *:c3 *:c4 *:d2 *:d3 *:d4 *:e2"
+
  edges="none"
 +
  visible="area(d1,a4,d4,e2,e1) area(a5,a7,b7,c6,c5)"
 +
   contents="R d1 e1 a5 c5 a7 c6 S area(d1,a4,d4,e2,e1)"
 
   />
 
   />
  
 
Some of the named interior templates can actually be viewed as interior versions of edge templates.  
 
Some of the named interior templates can actually be viewed as interior versions of edge templates.  
The bridge is an interior [[edge template II|template II]], the parallelogram is an interior [[Edge template III2a|template III-2-a]], and the span is an interior [[Edge template III2a|template III-2-b]].
+
The bridge is an interior [[edge template II|template II]], the parallelogram is an interior [[Edge template III2a|template III-2-a]], the span is an interior [[Edge template III2b|template III-2-b]], the crescent is an interior [[Edge_template_III2d|template III-2-d]], and the shopping cart is an interior [[Edge template III2g|template III-2-g]].
  
 
[[category:interior templates]]
 
[[category:interior templates]]

Latest revision as of 23:41, 14 February 2024

This page lists some interior templates. In each case, the carrier of the template consists of the cells that are shown in its diagram.

2- and 3-stone templates

The bridge

The wheel

4-stone templates

These templates are grouped by the size and shape of their carrier.

The trapezoid

The crescent

The span

The parallelogram

The box

The diamond

The shopping cart

ShoppingCart.png

The scooter

Scooter.png

The bicycle

Bicycle.png

The hammock

Hammock.png

This template is a variation of the diamond that only guarantees a connection between the two stones marked with arrows. It does not guarantee all 4 stones to be connected.

The wide parallelogram

Long version of templates

Several interior templates have "long" versions. These work at any length, and are basically interior versions of second row ladder escapes.

The long crescent

The long trapezoid

There are several ways of making a long trapezoid. Two of them are shown here:

The long span

The long span is relatively common as an edge template. The most common example of this is edge template V2-k:

ab

Note that the cells marked "a" and "b", which belong to the carrier of this template, are captured by Red, and therefore this really is an edge version of the long span. For the same reason, the following is an edge template as well:

Template extensions

Given a template, it is often possible to extend the template by adding one or more stones that threaten to connect to the template in two different ways. For example, the following 5-stone templates are extensions of the trapezoid. In each case, the trapezoid is shown in white and the extension in gray.

Because template extensions are so numerous, they usually do not get their own names, and it is not usually worth memorizing them as separate templates.

Interior templates from edge templates

Since a solid row of stones of the same color acts pretty much like an edge, all edge templates can also be used as interior templates. Such templates typically do not have their own name, but are named after the corresponding edge template. For example, here is an interior ziggurat:

To simulate an edge, it is not actually necessary to have a solid row of stones; it is sufficient that each cell on "row 1" of the edge is adjacent to a connected red stone. For example, the following is another variant of an interior ziggurat:

One can construct a virtually unlimited number of templates this way. Here is an example of an interior IV-2-a attached to a trapezoid:

Some of the named interior templates can actually be viewed as interior versions of edge templates. The bridge is an interior template II, the parallelogram is an interior template III-2-a, the span is an interior template III-2-b, the crescent is an interior template III-2-d, and the shopping cart is an interior template III-2-g.