List of bracketopes (Meta, 4)

From Hi.gher. Space

(Difference between revisions)
(created page)
(I got bored (again), so here's all the 5D bracketopes. As expected, there's 75 of them.)
 
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This is a '''list of [[bracketope]]s''' in dimensions from one to three.
+
<[#ontology [kind meta] [cats Bracketope]]>
 +
This is a '''list of [[bracketope]]s''' in dimensions from zero to five.
-
{|style="border: 1px solid; border-color:#808080; border-collapse: collapse;" cellpadding="2" width="100%"
+
<table class='shapelist' style='width: 100%;'><tr>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''Name'''
+
<th class='key' style='width: 20%;'>Name</th>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[[Rotopic index]]'''
+
<th class='key' style='width: 20%;'>[[Toratopic index]]</th>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[[Bracketopic index]]'''
+
<th class='key' style='width: 20%;'>[[Tapertopic index]]</th>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[[Bracket notation]]'''
+
<th class='key' style='width: 20%;'>[[Bracketopic index]]</th>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[[CSG notation]]'''
+
<th class='key' style='width: 20%;'>[[Bracket notation]]</th>
-
|-
+
</tr><tr>
-
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''1D bracketopes'''
+
<td class='cat' colspan='5'>0D bracketopes (total 1)</td>
-
|-
+
</tr><tr class='row1'>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Line (shape)|Line]]'''
+
<td class='key'>[[Point]]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1'''
+
<td>N/A</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''1'''
+
<td>0</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[x]'''
+
<td>0</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''E'''
+
<td>''Empty string''</td>
-
|-
+
</tr><tr>
-
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''2D bracketopes'''
+
<td class='cat' colspan='5'>1D bracketopes (total 1)</td>
-
|-
+
</tr><tr class='row1'>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Square]]'''
+
<td class='key'>[[Digon]]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''2'''
+
<td>N/A</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''2'''
+
<td>1</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[xy]'''
+
<td>1</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EE'''
+
<td>I</td>
-
|-
+
</tr><tr>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Diamond]]*'''
+
<td class='cat' colspan='5'>2D bracketopes (total 2)</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
+
</tr><tr class='row1'>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''3'''
+
<td class='key'>[[Square]]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<xy>'''
+
<td>1a</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ED'''
+
<td>3</td>
-
|-
+
<td>2</td>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Circle]]'''
+
<td>[II]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''4'''
+
</tr><tr class='row2'>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''4'''
+
<td class='key'>[[Circle]]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(xy)'''
+
<td>1b</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EL'''
+
<td>2</td>
-
|-
+
<td>3</td>
-
|valign="top" style="background-color:#bbbbff; text-align:center;" colspan="6"|'''3D bracketopes'''
+
<td>(II)</td>
-
|-
+
</tr><tr>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cube]]'''
+
<td class='cat' colspan='5'>3D bracketopes (total 6)</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''5'''
+
</tr><tr class='row1'>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''5'''
+
<td class='key'>[[Cube]]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[xyz]'''
+
<td>2a</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEE'''
+
<td>7</td>
-
|-
+
<td>4</td>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cuboid]]*'''
+
<td>[III]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
+
</tr><tr class='row2'>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''6'''
+
<td class='key'>[[Octahedron]]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[<xy>z]'''
+
<td>N/A</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EED'''
+
<td>N/A</td>
-
|-
+
<td>5</td>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Cylinder]]'''
+
<td><III></td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''11'''
+
</tr><tr class='row1'>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''7'''
+
<td class='key'>[[Sphere]]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''[(xy)z]'''
+
<td>2b</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EEL'''
+
<td>5</td>
-
|-
+
<td>6</td>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Wide octahedron]]*'''
+
<td>(III)</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
+
</tr><tr class='row2'>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''8'''
+
<td class='key'>[[Cylinder]]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<[xy]z>'''
+
<td>3a</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EED'''
+
<td>6</td>
-
|-
+
<td>7</td>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Octahedron]]'''
+
<td>[(II)I]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
+
</tr><tr class='row1'>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''9'''
+
<td class='key'>[[Bicone]]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<xyz>'''
+
<td>N/A</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EDD'''
+
<td>N/A</td>
-
|-
+
<td>8</td>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Bicone]]'''
+
<td><(II)I></td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
+
</tr><tr class='row2'>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''10'''
+
<td class='key'>[[Crind]]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''<(xy)z>'''
+
<td>N/A</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELD'''
+
<td>N/A</td>
-
|-
+
<td>9</td>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Crind]]'''
+
<td>([II]I)</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
+
</tr><tr>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''11'''
+
<td class='cat' colspan='5'>4D bracketopes (total 21)</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''([xy]z)'''
+
</tr><tr class='row1'>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''EL&LE'''
+
<td class='key'>[[Geochoron]]</td>
-
|-
+
<td>4a</td>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Narrow crind]]*'''
+
<td>16</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''N/A'''
+
<td>10</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''12'''
+
<td>[IIII]</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(<xy>z)'''
+
</tr><tr class='row2'>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''''Unknown'''''
+
<td class='key'>[[Aerochoron]]</td>
-
|-
+
<td>N/A</td>
-
|valign="top" width="20%" style="background-color:#ddddff; text-align:center;"|'''[[Sphere]]'''
+
<td>N/A</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''7'''
+
<td>11</td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''13'''
+
<td><IIII></td>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''(xyz)'''
+
</tr><tr class='row1'>
-
|valign="top" width="20%" style="background-color:#eeeeff; text-align:center;"|'''ELL'''
+
<td class='key'>[[Glome]]</td>
-
|}
+
<td>4b</td>
 +
<td>12</td>
 +
<td>12</td>
 +
<td>(IIII)</td>
 +
</tr><tr class='row2'>
 +
<td class='key'>[[Cubinder]]</td>
 +
<td>5a</td>
 +
<td>15</td>
 +
<td>13</td>
 +
<td>[(II)II]</td>
 +
</tr><tr class='row1'>
 +
<td class='key'>[[Dibicone]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>14</td>
 +
<td><(II)II></td>
 +
</tr><tr class='row2'>
 +
<td class='key'>[[Dicrind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>15</td>
 +
<td>([II]II)</td>
 +
</tr><tr class='row1'>
 +
<td class='key'>[[Octahedral prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>16</td>
 +
<td>[<III>I]</td>
 +
</tr><tr class='row2'>
 +
<td class='key'>[[Spherinder]]</td>
 +
<td>7a</td>
 +
<td>13</td>
 +
<td>17</td>
 +
<td>[(III)I]</td>
 +
</tr><tr class='row1'>
 +
<td class='key'>[[Cubic bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>18</td>
 +
<td><[III]I></td>
 +
</tr><tr class='row2'>
 +
<td class='key'>[[Bisphone]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>19</td>
 +
<td><(III)I></td>
 +
</tr><tr class='row1'>
 +
<td class='key'>[[Cubic crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>20</td>
 +
<td>([III]I)</td>
 +
</tr><tr class='row2'>
 +
<td class='key'>[[Octahedral crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>21</td>
 +
<td>(<III>I)</td>
 +
</tr><tr class='row1'>
 +
<td class='key'>[[Biconic prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>22</td>
 +
<td>[<(II)I>I]</td>
 +
</tr><tr class='row2'>
 +
<td class='key'>[[Crindal prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>23</td>
 +
<td>[([II]I)I]</td>
 +
</tr><tr class='row1'>
 +
<td class='key'>[[Bicylindrone]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>24</td>
 +
<td><[(II)I]I></td>
 +
</tr><tr class='row2'>
 +
<td class='key'>[[Crindal bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>25</td>
 +
<td><([II]I)I></td>
 +
</tr><tr class='row1'>
 +
<td class='key'>[[Cylindrical crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>26</td>
 +
<td>([(II)I]I)</td>
 +
</tr><tr class='row2'>
 +
<td class='key'>[[Biconic crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>27</td>
 +
<td>(<(II)I>I)</td>
 +
</tr><tr class='row1'>
 +
<td class='key'>[[Duocylinder]]</td>
 +
<td>6a</td>
 +
<td>14</td>
 +
<td>28</td>
 +
<td>[(II)(II)]</td>
 +
</tr><tr class='row2'>
 +
<td class='key'>[[Duocircular tegum]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>29</td>
 +
<td><(II)(II)></td>
 +
</tr><tr class='row1'>
 +
<td class='key'>[[Duocrind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>30</td>
 +
<td>([II][II])</td>
 +
</tr><tr>
 +
<td class='cat' colspan='5'>5D bracketopes (total 75)</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Geoteron]]</td>
 +
<td>9a</td>
 +
<td>36</td>
 +
<td>31</td>
 +
<td>[IIIII]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Aeroteron]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>32</td>
 +
<td><IIIII></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Pentasphere]]</td>
 +
<td>9b</td>
 +
<td>30</td>
 +
<td>33</td>
 +
<td>(IIIII)</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Tesserinder]]</td>
 +
<td>10a</td>
 +
<td>35</td>
 +
<td>34</td>
 +
<td>[(II)III]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Tribicone]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>35</td>
 +
<td><(II)III></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Tricrind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>36</td>
 +
<td>([II]III)</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Octahedral diprism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>37</td>
 +
<td>[<III>II]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Cubspherinder]]</td>
 +
<td>12a</td>
 +
<td>33</td>
 +
<td>38</td>
 +
<td>[(III)II]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Cubic dibipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>39</td>
 +
<td><[III]II></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Dibisphone]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>40</td>
 +
<td><(III)II></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Cubic dicrind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>41</td>
 +
<td>([III]II)</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Octahedral dicrind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>42</td>
 +
<td>(<III>II)</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Hexadecachoral prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>43</td>
 +
<td>[<IIII>I]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Glominder]]</td>
 +
<td>16a</td>
 +
<td>31</td>
 +
<td>44</td>
 +
<td>[(IIII)I]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Tesseractic bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>45</td>
 +
<td><[IIII]I></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Biglone]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>46</td>
 +
<td><(IIII)I></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Tesseractic crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>47</td>
 +
<td>([IIII]I)</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Hexadecachoral crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>48</td>
 +
<td>(<IIII>I)</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Biconic diprism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>49</td>
 +
<td>[<(II)I>II]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Crindal diprism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>50</td>
 +
<td>[([II]I)II]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Dibicylindrone]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>51</td>
 +
<td><[(II)I]II></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Crindal dibipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>52</td>
 +
<td><([II]I)II></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Cylindrical dicrind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>53</td>
 +
<td>([(II)I]II)</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Biconic dicrind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>54</td>
 +
<td>(<(II)I>II)</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Dibiconic prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>55</td>
 +
<td>[<(II)II>I]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Dicrindal prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>56</td>
 +
<td>[([II]II)I]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Bicubindrone]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>57</td>
 +
<td><[(II)II]I></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Dicrindal bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>58</td>
 +
<td><([II]II)I></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Cubindrical crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>59</td>
 +
<td>([(II)II]I)</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Dibiconic crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>60</td>
 +
<td>(<(II)II>I)</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Cubic bipyramidal prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>61</td>
 +
<td>[<[III]I>I]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Bisphonic prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>62</td>
 +
<td>[<(III)I>I]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Cubic crindal prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>63</td>
 +
<td>[([III]I)I]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Octahedral crindal prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>64</td>
 +
<td>[(<III>I)I]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Octahedral prismatic bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>65</td>
 +
<td><[<III>I]I></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Bispherindrone]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>66</td>
 +
<td><[(III)I]I></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Cubic crindal bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>67</td>
 +
<td><([III]I)I></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Octahedral crindal bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>68</td>
 +
<td><(<III>I)I></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Octahedral prismatic crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>69</td>
 +
<td>([<III>I]I)</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Spherindrical crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>70</td>
 +
<td>([(III)I]I)</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Cubic bipyramidal crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>71</td>
 +
<td>(<[III]I>I)</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Bisphonic crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>72</td>
 +
<td>(<(III)I>I)</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Bicylindronic prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>73</td>
 +
<td>[<[(II)I]I>I]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Crindal bipyramidal prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>74</td>
 +
<td>[<([II]I)I>I]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Cylindrical crindal prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>75</td>
 +
<td>[([(II)I]I)I]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Biconic crindal prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>76</td>
 +
<td>[(<(II)I>I)I]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Biconic prismatic bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>77</td>
 +
<td><[<(II)I>I]I></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Crindal prismatic bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>78</td>
 +
<td><[([II]I)I]I></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Cylindrical crindal bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>79</td>
 +
<td><([(II)I]I)I></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Biconic crindal bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>80</td>
 +
<td><(<(II)I>I)I></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Biconic prismatic crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>81</td>
 +
<td>([<(II)I>I]I)</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Crindal prismatic crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>82</td>
 +
<td>([([II]I)I]I)</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Bicylindronic crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>83</td>
 +
<td>(<[(II)I]I>I)</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Crindal bipyramidal crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>84</td>
 +
<td>(<([II]I)I>I)</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Duocyldyinder]]</td>
 +
<td>11a</td>
 +
<td>34</td>
 +
<td>85</td>
 +
<td>[(II)(II)I]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Duocircular tegmal bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>86</td>
 +
<td><(II)(II)I></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Duocrindal crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>87</td>
 +
<td>([II][II]I)</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Duocircular tegmal prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>88>/td>
 +
<td>[<(II)(II)>I]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Duocrindal prism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>89</td>
 +
<td>[([II][II])I]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Biduocylindrone]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>90</td>
 +
<td><[(II)(II)]I></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Duocrindal bipyramid]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>91</td>
 +
<td><([II][II])I></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Duocylindrical crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>92</td>
 +
<td>([(II)(II)]I)</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Duocircular tegmal crind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>93</td>
 +
<td>(<(II)(II)>I)</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Cyloctahedrinder]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>94</td>
 +
<td>[<III>(II)]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Cylspherinder]]</td>
 +
<td>14a</td>
 +
<td>32</td>
 +
<td>95</td>
 +
<td>[(III)(II)]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Circle/cube duotegum]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>96</td>
 +
<td><[III](II)></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Circle/sphere duotegum]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>97</td>
 +
<td><(III)(II)></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Square/cube duocrind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>98</td>
 +
<td>([III][II])</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Square/octahedron duocrind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>99</td>
 +
<td>(<III>[II])</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Circle/bicone duoprism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>100</td>
 +
<td>[<(II)I>(II)]</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Circle/crind duoprism]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>101</td>
 +
<td>[([II]I)(II)]</td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[Circle/cylinder duotegum]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>102</td>
 +
<td><[(II)I](II)></td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Circle/crind duotegum]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>103</td>
 +
<td><([II]I)(II)></td>
 +
</tr>
 +
<tr class='row2'>
 +
<td class='key'>[[square/cylinder duocrind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>104</td>
 +
<td>([(II)I][II])</td>
 +
</tr>
 +
<tr class='row1'>
 +
<td class='key'>[[Square/bicone duocrind]]</td>
 +
<td>N/A</td>
 +
<td>N/A</td>
 +
<td>105</td>
 +
<td>(<(II)I>[II])</td>
 +
</tr>
 +
</table>

Latest revision as of 20:42, 18 February 2019

This is a list of bracketopes in dimensions from zero to five.

Name Toratopic index Tapertopic index Bracketopic index Bracket notation
0D bracketopes (total 1)
Point N/A 0 0 Empty string
1D bracketopes (total 1)
Digon N/A 1 1 I
2D bracketopes (total 2)
Square 1a 3 2 [II]
Circle 1b 2 3 (II)
3D bracketopes (total 6)
Cube 2a 7 4 [III]
Octahedron N/A N/A 5 <III>
Sphere 2b 5 6 (III)
Cylinder 3a 6 7 [(II)I]
Bicone N/A N/A 8 <(II)I>
Crind N/A N/A 9 ([II]I)
4D bracketopes (total 21)
Geochoron 4a 16 10 [IIII]
Aerochoron N/A N/A 11 <IIII>
Glome 4b 12 12 (IIII)
Cubinder 5a 15 13 [(II)II]
Dibicone N/A N/A 14 <(II)II>
Dicrind N/A N/A 15 ([II]II)
Octahedral prism N/A N/A 16 [<III>I]
Spherinder 7a 13 17 [(III)I]
Cubic bipyramid N/A N/A 18 <[III]I>
Bisphone N/A N/A 19 <(III)I>
Cubic crind N/A N/A 20 ([III]I)
Octahedral crind N/A N/A 21 (<III>I)
Biconic prism N/A N/A 22 [<(II)I>I]
Crindal prism N/A N/A 23 [([II]I)I]
Bicylindrone N/A N/A 24 <[(II)I]I>
Crindal bipyramid N/A N/A 25 <([II]I)I>
Cylindrical crind N/A N/A 26 ([(II)I]I)
Biconic crind N/A N/A 27 (<(II)I>I)
Duocylinder 6a 14 28 [(II)(II)]
Duocircular tegum N/A N/A 29 <(II)(II)>
Duocrind N/A N/A 30 ([II][II])
5D bracketopes (total 75)
Geoteron 9a 36 31 [IIIII]
Aeroteron N/A N/A 32 <IIIII>
Pentasphere 9b 30 33 (IIIII)
Tesserinder 10a 35 34 [(II)III]
Tribicone N/A N/A 35 <(II)III>
Tricrind N/A N/A 36 ([II]III)
Octahedral diprism N/A N/A 37 [<III>II]
Cubspherinder 12a 33 38 [(III)II]
Cubic dibipyramid N/A N/A 39 <[III]II>
Dibisphone N/A N/A 40 <(III)II>
Cubic dicrind N/A N/A 41 ([III]II)
Octahedral dicrind N/A N/A 42 (<III>II)
Hexadecachoral prism N/A N/A 43 [<IIII>I]
Glominder 16a 31 44 [(IIII)I]
Tesseractic bipyramid N/A N/A 45 <[IIII]I>
Biglone N/A N/A 46 <(IIII)I>
Tesseractic crind N/A N/A 47 ([IIII]I)
Hexadecachoral crind N/A N/A 48 (<IIII>I)
Biconic diprism N/A N/A 49 [<(II)I>II]
Crindal diprism N/A N/A 50 [([II]I)II]
Dibicylindrone N/A N/A 51 <[(II)I]II>
Crindal dibipyramid N/A N/A 52 <([II]I)II>
Cylindrical dicrind N/A N/A 53 ([(II)I]II)
Biconic dicrind N/A N/A 54 (<(II)I>II)
Dibiconic prism N/A N/A 55 [<(II)II>I]
Dicrindal prism N/A N/A 56 [([II]II)I]
Bicubindrone N/A N/A 57 <[(II)II]I>
Dicrindal bipyramid N/A N/A 58 <([II]II)I>
Cubindrical crind N/A N/A 59 ([(II)II]I)
Dibiconic crind N/A N/A 60 (<(II)II>I)
Cubic bipyramidal prism N/A N/A 61 [<[III]I>I]
Bisphonic prism N/A N/A 62 [<(III)I>I]
Cubic crindal prism N/A N/A 63 [([III]I)I]
Octahedral crindal prism N/A N/A 64 [(<III>I)I]
Octahedral prismatic bipyramid N/A N/A 65 <[<III>I]I>
Bispherindrone N/A N/A 66 <[(III)I]I>
Cubic crindal bipyramid N/A N/A 67 <([III]I)I>
Octahedral crindal bipyramid N/A N/A 68 <(<III>I)I>
Octahedral prismatic crind N/A N/A 69 ([<III>I]I)
Spherindrical crind N/A N/A 70 ([(III)I]I)
Cubic bipyramidal crind N/A N/A 71 (<[III]I>I)
Bisphonic crind N/A N/A 72 (<(III)I>I)
Bicylindronic prism N/A N/A 73 [<[(II)I]I>I]
Crindal bipyramidal prism N/A N/A 74 [<([II]I)I>I]
Cylindrical crindal prism N/A N/A 75 [([(II)I]I)I]
Biconic crindal prism N/A N/A 76 [(<(II)I>I)I]
Biconic prismatic bipyramid N/A N/A 77 <[<(II)I>I]I>
Crindal prismatic bipyramid N/A N/A 78 <[([II]I)I]I>
Cylindrical crindal bipyramid N/A N/A 79 <([(II)I]I)I>
Biconic crindal bipyramid N/A N/A 80 <(<(II)I>I)I>
Biconic prismatic crind N/A N/A 81 ([<(II)I>I]I)
Crindal prismatic crind N/A N/A 82 ([([II]I)I]I)
Bicylindronic crind N/A N/A 83 (<[(II)I]I>I)
Crindal bipyramidal crind N/A N/A 84 (<([II]I)I>I)
Duocyldyinder 11a 34 85 [(II)(II)I]
Duocircular tegmal bipyramid N/A N/A 86 <(II)(II)I>
Duocrindal crind N/A N/A 87 ([II][II]I)
Duocircular tegmal prism N/A N/A 88>/td> [<(II)(II)>I]
Duocrindal prism N/A N/A 89 [([II][II])I]
Biduocylindrone N/A N/A 90 <[(II)(II)]I>
Duocrindal bipyramid N/A N/A 91 <([II][II])I>
Duocylindrical crind N/A N/A 92 ([(II)(II)]I)
Duocircular tegmal crind N/A N/A 93 (<(II)(II)>I)
Cyloctahedrinder N/A N/A 94 [<III>(II)]
Cylspherinder 14a 32 95 [(III)(II)]
Circle/cube duotegum N/A N/A 96 <[III](II)>
Circle/sphere duotegum N/A N/A 97 <(III)(II)>
Square/cube duocrind N/A N/A 98 ([III][II])
Square/octahedron duocrind N/A N/A 99 (<III>[II])
Circle/bicone duoprism N/A N/A 100 [<(II)I>(II)]
Circle/crind duoprism N/A N/A 101 [([II]I)(II)]
Circle/cylinder duotegum N/A N/A 102 <[(II)I](II)>
Circle/crind duotegum N/A N/A 103 <([II]I)(II)>
square/cylinder duocrind N/A N/A 104 ([(II)I][II])
Square/bicone duocrind N/A N/A 105 (<(II)I>[II])