Square pucofastegium

Square pucofastegium
Rank	4
Type	Segmentotope
Notation
Bowers style acronym	Squipuf
Coxeter diagram	ox ox4xx&#x
Elements
Cells	4 square pyramids, 4 triangular prisms, 2 square cupolas, 1 octagonal prism
Faces	8+8 triangles, 1+4+4+8 squares, 2 octagons
Edges	4+8+8+8+16
Vertices	4+16
Vertex figures	4 wedges, edge lengths 1 (base square) and √2 (top and side edges)
	16 irregular tetrahedra, edge lengths 1 (2), √2 (3), and √2+√2 (1)
Measures (edge length 1)
Circumradius	${\sqrt {2+{\sqrt {2}}}}\approx 1.84776$
Hypervolume	${\frac {9+8{\sqrt {2}}}{24}}\approx 0.84640$
Dichoral angles	Squippy–3–trip: 150º
	Squacu–4–trip: $\arccos \left(-{\frac {\sqrt {6}}{3}}\right)\approx 144.73561^{\circ }$
	Squippy–3–squacu: 120º
	Squacu–4–squacu: 90º
	Op–8–squacu: 45º
	Op–4–squippy: 45º
	Trip–4–op: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
Heights	Oc atop squacu: ${\frac {\sqrt {2}}{2}}\approx 0.70711$
	Square atop op: ${\frac {1}{2}}=0.5$
Central density	1
Related polytopes
Army	Squipuf
Regiment	Squipuf
Dual	Square pucolanotch
Conjugate	Retrograde square pucofastegium
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B2×A1×I, order 16
Convex	Yes
Nature	Tame

The square pucofastegium, or squipuf, also sometimes called the square magnabicupolic ring, is a CRF segmentochoron (designated K-4.105 on Richard Klitzing's list). It consists of 4 triangular prisms, 4 square pyramids, 2 square cupolas, and 1 octagonal prism.

The square pucofastegium occurs as the square-first cap of the small rhombated tesseract. In fact diminishing 8 such caps from the small rhombated tesseract results in the octagonal duoprism.

Vertex coordinates

The vertices of a square pucofastegium with edge length 1 are given by:

• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,{\frac {1}{2}}\right),$
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,0\right),$
• $\left(\pm {\frac {1+{\sqrt {2}}}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0\right).$

Representations

A square pucofastegium has the following Coxeter diagrams:

• ox ox4xx&#x (full symmetry)
• xxx4oxx&#x (BC2 symmetry only, seen with octagon atop square cupola)

External links

• Klitzing, Richard. "squipuf".
• Quickfur. "The Square Magnabicupolic Ring".