pentagonal trapezohedron

File:Ten D10s.jpg

The pentagonal trapezohedron was patented for use as a gaming die (i.e. "game apparatus") in 1906.{{US patent|809293}} These dice are used for role-playing games that use percentile-based skills; however, a twenty-sided die can be labeled with the numbers 0-9 twice to use for percentages instead.

Subsequent patents on ten-sided dice have made minor refinements to the basic design by rounding or truncating the edges. This enables the die to tumble so that the outcome is less predictable. One such refinement became notorious at the 1980 Gen Con{{cite web |url=http://planescape.outshine.com/official.planescape-torment.org/oldnews/greg_0507.html |archiveurl=https://web.archive.org/web/20160814000600/http://planescape.outshine.com/official.planescape-torment.org/oldnews/greg_0507.html |archivedate=2016-08-14 |title=Greg Peterson about Gen Con 1980: The big news of the year was that someone had 'invented' the ten-sided die.}} when the patent was incorrectly thought to cover ten-sided dice in general.

Ten-sided dice are commonly numbered from 0 to 9, as this allows two to be rolled in order to easily obtain a percentile result. Where one die represents the 'tens', the other represents 'units' therefore a result of 7 on the former and 0 on the latter would be combined to produce 70. A result of double-zero is commonly interpreted as 100. Some ten-sided dice (often called 'Percentile Dice') are sold in sets of two where one is numbered from 0 to 9 and the other from 00 to 90 in increments of 10, thus making it impossible to misinterpret which one is the tens and which the units die. Ten-sided dice may also be marked 1 to 10 when a random number in this range is desirable.

The pentagonal trapezohedron also exists as a spherical tiling, with 2 vertices on the poles, and alternating vertices equally spaced above and below the equator.

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{{Trapezohedra}}

• {{cite book |last1=Cundy |first1=H. M. |last2=Rollett |first2=A. P. |year=1981 |title=Mathematical models|title-link=Mathematical Models (Cundy and Rollett) |edition=3rd |publisher=Tarquin |page=117}}
• {{cite book

| last1 = Alsina | first1 = Claudi

| last2 = Nelsen | first2 = Roger B.

| contribution = Section 3.4: Kites

| contribution-url = https://books.google.com/books?id=CGDSDwAAQBAJ

| isbn = 978-1-4704-5312-1

| location = Providence, Rhode Island

| mr = 4286138

| pages = 73–78

| publisher = MAA Press and American Mathematical Society

| series = The Dolciani Mathematical Expositions

| title = A Cornucopia of Quadrilaterals

| volume = 55

| year = 2020

}}

• [https://www.academia.edu/11805176/Mathematical_analysis_of_uniform_polyhedron_trapezohedron_having_2n_congruent_right_kite_faces_4n_edges_and_2n_2_vertices_lying_on_a_spherical_surface_generalized_formula_for_uniform_polyhedrons_with_congruent_right_kite_faces_ Generalized formula of uniform polyhedron (trapezohedron) having 2n congruent right kite faces] from Academia.edu
• {{mathworld | urlname = Trapezohedron | title = Trapezohedron}}
• [http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] www.georgehart.com: The Encyclopedia of Polyhedra
• VRML [http://www.georgehart.com/virtual-polyhedra/vrml/pentagonal_trapezohedron.wrl model] {{Webarchive|url=https://web.archive.org/web/20180224035822/http://www.georgehart.com/virtual-polyhedra/vrml/pentagonal_trapezohedron.wrl |date=2018-02-24 }}
• [http://www.georgehart.com/virtual-polyhedra/conway_notation.html Conway Notation for Polyhedra] Try: "dA5"

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Category:Dice

Category:Polyhedra

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