Triangular prismic pyramid (EntityTopic, 14)

(Difference between revisions)

Latest revision as of 18:58, 27 March 2014

The triangular prismic pyramid is a CRF polychoron among Klitzing's segmentochora (K4.7).

It can be Stott-expanded into the triangular magnabicupolic ring.

# Triangular prism
<±1, -1/√3, ±1, 0>
<0, 2/√3, ±1, 0>

# Apex
<0, 0, 0, sqrt(5/3)>

Notable Tetrashapes
Regular:	pyrochoron • aerochoron • geochoron • xylochoron • hydrochoron • cosmochoron
Powertopes:	triangular octagoltriate • square octagoltriate • hexagonal octagoltriate • octagonal octagoltriate
Circular:	glome • cubinder • duocylinder • spherinder • sphone • cylindrone • dicone • coninder
Torii:	tiger • torisphere • spheritorus • torinder • ditorus

26. 11² Tetrahedral prism	27. [11¹]¹ Triangular prismic pyramid	28. 1³ Pentachoron
List of tapertopes

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+<[#ontology [kind topic] [cats 4D Tapertope Polytope Pyramid]]>
 {{STS Shape
 | dim=4
+| image=<[#embed [hash CJ00T6X0STHD03FYVMVX6MQ2ZT] [width 180]]>
 | elements=6, 14, 15, 7
 | ssc2=&+G3
@@ Line 8: / Line 10: @@
 | index=27
 }}}}
+The '''triangular prismic pyramid''' is a [[CRF polychoron]] among Klitzing's [[segmentochora]] (K4.7).
+It can be Stott-expanded into the [[triangular magnabicupolic ring]].
+==Dichoral angles==
+* Between triangular prism and square pyramid: atan(√5) ≈ 65.9051574479°
+* Between triangular prism and tetrahedron: atan(√(5/3)) ≈ 52.2387560930°
+* Between square pyramid and tetrahedron: 103.6330222254°
+==Coordinates==
+<pre>
+# Triangular prism
+<±1, -1/√3, ±1, 0>
+<0, 2/√3, ±1, 0>
+# Apex
+<0, 0, 0, sqrt(5/3)>
+</pre>
 {{Tetrashapes}}
 {{Tapertope Nav|26|27|28|11<sup>2</sup><br>Tetrahedral prism|[11<sup>1</sup>]<sup>1</sup><br>Triangular prismic pyramid|1<sup>3</sup><br>Pentachoron|chora}}
-[[Category:Uniform prismachora]]