US1292188A - Blank for forming hollow polyhedrons. - Google Patents

Description

A. H. WHEELER. BLANK FOR FORMING HOLLOW POLYHEADRO NS.

APPLICATION FILED MAR. 4. 19-18...

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ALBERT HARRY XVI-IEELER, OF WORCESTER, MASSACHUSETTS.

-BLANK FOB. FORMING HOLLOW POLYHEDRONS.

Specification of Letters Patent.

Patented Jan. 21, 1919.

, Application filed March 4, 1918. Serial No. 220.202.

To all whom z't may concern:

Be it known that I, ALBERT HARRY WHEELER, a citizen of the United States, residing at Worcester, in the county of WVorcester and State of Massachusetts, have invented a new and useful Blank for Forming HollowPolyhedl-ons, of which the following is a specification.

This inveiition relates to the construction of polyhedrons of sheet material in a simple and convenientway for the purpose of demonstrating principles of solid geometry in the Classroom and for similar purposes.

The principal objects of the invention are to provide a construction of a blank from sheet material, as for example, paper which can 'be manipulated in a certain way so as to produce a hollow polyhedron; to provide constructions connected therewith for effectively holding the parts together at the angles, and of such a nature that no projecting parts come outside the hollow figure when it is completed, thus producing a new article of manufacture in the polyhedron itself; and to provide an improved hinge connection for pivotally joining two pieces of sheet material so that the blank need not be formed of a single piece, but can be formed of several if desired. This construction is also capable of use independently of lthe production of polyhedrons. Further objects and advantages of the invention will appear hereinafter.

Reference is to be had to the accompanying drawings, in which- Figure 1 is a plan view of a blank shown in three pieces for forming a regular dodecahedron;

Fig. 2 is a plan of one end of said blank showing some of the adjacent faces as secured in position to illustrate the manner in which the blank is manipulated to start to form the solid figure, the faces of the blank not yet connected being broken away;

Fig. 3 is a view similar to Fig. 2 showing in direct plan a half of the figure completed and the remainder of the faces also connected together to form the other half of the figure but being bent off to one side so as to give a view of the interior of the first mentioned half and showingI the way in which the faces are held in position at Vthe angles;

Fig. 4 is a view of a complete dodecahedron in front elevation;

Fig. 5 is a view similar to Fig. 1 of a blank arranged for forming an irregular pol hedron formed of six square sides and eight triangular ones;

Fig. 6 is a front elevation of the completed polyhedron which is in reality a cube with the six corners truncated in a regular manner;

Fig. 7 is a fragmentary view of a pair of faces or sheets showing a modified form of hinge, and

Fig. 8 is a. similar view showing another form.

In the form of the invention shown in the first four figures a blank is provided consisting of three pieces A, B, C. Each one of these pieces, and in fact the entire blank is made up of a plurality of regular polyo-ons, in this case pentagons, each one destined to constitute one face of the dodecahedron shown in Fig. 4. It is to be understood that this blank can be all in one piece as shown in Fig. 5, but three pieces are illustrated here for convenience.

For the moment, ignoring the manner of connectino' these three pieces and assuming them to be all connected so that they act as a single sheet, all the twelve faces of which are integral with each other and constitute a continuous series, it will be seen that each of these faces is connected with the next one along a straight line which constitutes one of its edges. These connections are integral except in two places in the form illustrated and they all constitute hinges about which the faces 'can be bent with respect to each other. It will be seen also that each of the faces is provided with either one or two projecting holding or fastening tabs D.

It is to be observed that, each of the angles of the pentagon being one hundred and eight degrees, the several angles d, that is the obtuse angles formed between the adj acent edges of the polygon face and the respcctive tabs D are shown the same, that is one hundred and eight degrees in order to foim a contact with the inside face of theV next face. This gives a maximum holding force but it is to be understood that these' angles can be smaller so long as the distance between the two tip ends of a tab is greater than the length of the corresponding edge of the polygon. The location of these several tabs is such that either the ends of two 'edge of the base.

up in the same way against the other tabl D1, on face 1 and face '6 is brought around tabs on one face or the end of one tab on one face and of another tab on the next face are located at the opposite ends of each of the hinged edges of the polvgon. p

I have numbered the several polygonsof this figure from 1 to 12 inclusive, indicating the order in which they can be fold'ed-up although the figure can be constructed in the reverse order. Face l can be considered as the base of the dodecahedron to be produced. Tn order to form the figure the face numbered 2 is turned un out of. the plane o'fcthe 'basel and brought of course'to the necessary angle which need not be' stated o'rcalculated because the configuration of the parts is such that it will not lockin position at any other angle. This is the only thing necessary at that time. This havingbtfen accomplished the face numberedv 3 is bent about its hinge connecting it with face 2 to the position in which it makes the same angle with the .base as' face 2. In doing this it will be observed that the 'tab D' on face 1 is brought up inside face 3 and the location of this face, in the form shown, in position with its lower edge contacting with the horizontal edge of the base 1 causes this tab D' to hold the. above mentioned position with a maximum ofl efficiency. Now the tab D4 on the next face at the bottom, which just before the last inotion mentioned had to be folded back' against the inside of the face, can now be brought out into horizontal position'on the base 1 and` the. face D4 swung around until its lower edge contacts with the third Now face 5- is brought and its tab D6 is also brought into horizontal position and the faces are locked in that place by bringing the tab D2 inside of the face 6, sothat its lower edge which is now'horizontal projects over the tab D6' The and holds it in horizontal position.

tab D4 holds the tabs D1 and D1 up in their` inclined positions against the inside surfaces of their respective faces 3 and 5, this tab D4 being horizontal and in contact with the base 1. The reason for making the angles alone hundred and eight 'degrees will:

now be apparent. The end edges of all the tabs D1, D1, D4 and D? fit against faces or tabs that at'their margins have to make thisV angle with the adjacent faces in the form'show'n in Figs. 1 to 4;

These six faces are now 'in theposition' shown in'Fig. 3 in plan. vThat figure is a little misleading because the otherhalf of the solid figure is not made usually independentlyl but the figure is made progressively all the way in accordance with the numbering on the faces. It isV shown merely' in this way for illustrating where the faces and tabs are located when the figureis half done and it incidentally shows certain things about the rest of the figure. It is true, however, that the' whole dodecahedron can be shown as constructed in that figure and then the parts united.

Now the face 7 is bent inwardly toward the center of the figure in ordinary construction, and its tab D7 locked in between the two tabs D2 and D2 and the rest of the figure is formed progressively as stated until the* last side numbered 12 is brought into position and there the last tab D12 is tucled in behind the edge of thetab D,L0 at one end and thevtab D9 at theother to V,complete the figure. VVe 'get the 'dodecahedronfas shown in Fig. 11 in which it 'will beseen 'that there is no indication outside' that 'there isb any' fastenin'g means for holding the faces together', all the' tabs'beingby concealed inside. This is one of the objects of thei'inventiion and renders the resu'l'ting product 'a convenient one for use for demonstrating purposes', but it'wi'll beseen that in'spite of the concealment of the fastening tabs they thoroughly fasten the parts ini position on account of their Vangular relation to the faces and *iength 'I 4 I might remark'at' this point that this identity 'in angles is not necessary even when the regular polyhedron is constructed and would have to be modified inl 'casevof an ir-' regular polyh'edron. I have shownl the tab D12 as made of two pieces to facilitate'bending'it to complete the figure. V

In the first four figures Il have shown the pieces A and C separately hinged to the piece B by a hinge construction. 'In' this case the hinge constructionl consists simply of two hinge tabs E' extending'from each of'the faces, each tab being shown as of a general rectangular form and having a space E' separating them. Immediatelynnder each tab E at one xedge there is a"slit e. These slits are for receiving thecorresponding tabs on the other face.l :The distance from' the 4solid left end E'Iof'the right lhand tab E to the opposite'end of the left hand slot e adjacent to it 'on the face 10 `is'eouial to the length Vof the line by whichT the' left hand tab E is connected with the' face 11,' and the saine 'relationship is true of course for' the f other tabs. .'Therefore in'v` puttingf these tabs together when'the ytwo` faces lare placed back to back'they canbe slid together'l in the plane, being first folded'on'each `other until the back of th'eftab ,Eon the face 10 substantially coincideswith the correspondt ing line,that is the line c' onithe tab on the face' 11.3' 'This requires fno 'bending .or distortion ofthe faces yat'all. `Now?if'the'' two faces 10 and 11 are lfol'ded vup'on eachf other throughv any angle whatever, it will'. be found that these two'jedges'e' will slip) by each other and Vwe 'have athing'e connec-f out tearing or very badly distorting the parts unless the two faces 10 and 11 are folded together in contact, in which case the two edges e" can, if not naturally past each other, be brought past each other and then the two parts slid by with a transverse sliding motion. ItV is to be 'noted that the angle between the line between the tab E and the member 10, that is the line on which it is hinged, and the edge e' is reater than the one the hinge line makes with the edge of the slot E which happens in this case to be zero.A This shows up better in Fig. 7 where the *latter angle is an acute one. This furnishes a stop to prevent lthe parts separating in all positions of the two sheets which are hinged together except the one in which they are turned over into contact with each other.l

' In Figs. 7 and 8 other forms of hinge are shown embo'dying the same principles. In Fig. 7 these princ1ples are shown but in such form that the tabs F are without any slits but Vare 'simply made in the form of a trapezoid, in which the principles set forth above are carried out, the parts being assembled and taken apart in lthe same way as above described.

In Fig. 8 the tabs G are made in different form, but the relative dimensions and arrangements are the same as in Fig. 1, only the tabs instead of being the same length are formed one long and the other short, and they are shown as cut away near the center simply to avoid the presence of surplus material.

In Figs. 5 and 6 the construction of 'an irregular polyhedron is shown, the faces of the same being made up of squares and triangles, and in this case the tabs are shown provided with end angles of siXty degrees the same as those of the triangular faces. This blank also is difierent from the one shown in the first four figures, because the parts are all one integral whole, but that is not a feature peculiar to this figure as the same thing could be accomplished with the form shown in those figures. For that reason this construction will not be described in detail.

Although I have shown the invention as applied to one particular regular polyhedron and one irregular one I am aware of the fact that it can be applied to the construction of various regular and irregular polyhedrons without change in principle, only such changes in the angles and relations as are necessary to provide for different shapes.

Although I have illustrated and described only certain definite forms of the invention I am aware of the fact that modifications can be made therein by any person skilled in the art without departing from the scope of the invention as expressed in the claims. Therefore I do not wish to be limited to the construction of any definite figure or to all the details of construction, but what I do claim is 1. A blank of sheet material for use in constructing a hollow polyhedron, said blank being shaped to provide the number of polygonal faces necessary to produce the desired shape, said faces being flexibly connected with each other in a continuous series, the line of connection in each case being along one of the edges of the face, said faces having flexibly connected tabs extending beyond the boundaries of the respective polygons at the ends of said lines of connection to hold the faces together.

2. A blank for use in producing a polyhedron made up of a number of polygonal faces, each connected to another one along an edge by a flexible connection constituting a hinge, and a projecting hinged tab at each end of the hinge, each tab being adapted to fit against the surface of an adjacent face when the figure is completed to hold the faces in position.

3. A blank of sheet material for use in constructing a hollow polyhedron shaped to provide the number of regular polygonal faces necessary to produce the desired shape, said faces being flexibly and integrally connected with each other in a continuous integral series along the edges of the faces, and tabs flexibly connected with the several faces and having ends extending beyond the ends of the faces for the purpose of folding inside the adjacent faces and holding them in position.

4. A blank of'sheet material for use in constructing a hollow polyhedron comprising the number of polygonal faces necessary to produce the desired shape, said faces being flexibly connected with each other, said faces having flexibly connected tabs extending beyond the boundaries of the respective polygons at the ends of the lines of connection, certain of said tabs having their ends projecting beyond the line with which they are connected to the face so as to fold in behind an adjacent face.

5. A blank for use in producing a polyhedron made up of a number of polygonal faces, each connected to another one along an edge by a flexible connection constituting a hinge, one or both of each two adjacent faces having a projecting hinged tab at the end of the hinge adapted to fold behind the inner surface of an adjacent face when the figure is completed, to help hold the faces in position, one of said tabs having its ends forming projections located a distance apart greater than the length of the hinge line at the edge thereof by which said tab is connected with the adjacent faces.

6. A blank of sheet material for use in eonstructing a hollow polyhedron, shaped to provide the number of polygonal faces necessary to produce the desired, shape, said faces being flexibly connected withV each other and having fl'exibly: connected tabs ei;- tending beyond the boundaries of. the respective polygons at thefiends' of'the` lines of vconnection,one of said faces being 'sepa'f i'ably 'connected with another and adapted to swing about. the 'separable'connection as a,

'1 in 'f' ,it V

` 7. A blank for use in producing av polyhedron madeup ofial number of'` polygonal faces, each connected to *"'anothe'r one; along an 'edge by 'a flexible 'connection`-constitlitiiig a hin'ge; said' hinfge' compris'i'ng'g':twoftabsb eXfj tending from each' face,' said tabsfbe'in'g sep',-v arated from each other'and 'having'ia'space for' the reception of a tab on the otherxface, means 'Wherebyi the' 'two' faeS. when in Vconf tact fwith each other can be `moved .togetlflelI by a' Vmotion in aV plane until the rear lends of the respective tabs come into contact and pass each other and then the twoV faces will be hingedly vco'nnlebzcted with each: other,` one or both of each'itwo vadjacent,faces having a projecting hinged tab, atfthe `end of the hinge adapted to fit against I theI siirfa'ce of an adjacent face vwhenV vthe `figure is comf pleted to help hold the faces in position,"

8. lA body of sheet `material co'mpri's'ing two members or faces eachfpoflthem having two tabs projecting therefromjin the plane thereof,b the space between "the ,two tabsfjon each one, along the straight ,boundary line between the vmember and :the tabs, being equal to the' lengthV of a tabonfthe other piece so that the two members can be united by placing them in contact and moving them together with the 'forwardedge Aof each `rtab guide'd'behind the adjacent edgefof the correspondingtab onthe other member until the rear edge of ,the forward tab on'each member coincides with the rear edge of the tab'on' the other member and whereby the' two'lmembelfjli'e fihlls hinged 'together and' readily) Separebla Without,1hex1di1ie=r-whenfin,

that., one position.

"10. AT hollQw. pelyhedmn closetV @a all sides formedjdf .sheetfmaterial l'andr provided With fatening meanslocated;elitirelyiinside it', atrthe: ends .ofgsornefofrits edgesffand con'.-V sti-tebingV Coatinuatipns fat the anda- 1f:-S0nf1e.A

11. As,r articlewrof: mannfacture; a l body comprising two parts, formed'of, sheet lInfa-` tei'ial, having av hinge', connectionyybetween them comprising. Itwo tabs ,ony eacnhnone,v the body of .each tabbeinglongenthanfthe6 neck.

which3 joins, vit vto V,themaiii partof :the sheet materialfsaidtabsfionflach Part. fbeing :Spacedf apart to Vpermit the t. entrance between I them.

of aftab On'th/Otheripart.

As .article of manufacture,, aL body compris'ing two parts, formed of sheet l:material', having a ,y b hingei connection I. between them' comprisingutwo, spaced Ytabsxon each, thev .body of, each. tab being; longerthanfthe neckwhichfjoins it .tothe .mainfpart :of the Y sheet Lmatferial'yt the correspondingiedges vof,

saiditabsj being yparallel and foneof each' having an `edge.,,crossing a j correspondingy edge on a tab of the other part andlocated at, an anglezto the ,outerr zedges of the sheet and constituting ,,a stop, `.to prevent; theiry separation, exceptxwhen theutwo, partsv are folded back f into contact. fwith beachb other.`

Invtestimony whereof I :have hereunto aflixped my signature.

ALBERT [HeamnwHEELER-fifl Copies of this patent may leep obtained for `fivex cents each, by gddressing themf'CommissipneggofAgatents,`

i r,, .I V

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